CV

1. Curriculum Vitae
CRISTIAN ENACHE
Office Address: Department of Mathematics and Statistics, Laval University
1045, av. de la Medecine, Quebec, QC G1V 0A6, Canada
Home Address: 3315 Rue France-Prime, App. 207, Quebec, QC G1W 4X3, Canada
Phone: +1 (418) 656-2131 Ext. 5660 (work), +1 (418) 478-3898 (home)
Email Address: cenache23@yahoo.com
Homepage: https://www.researchgate.net/profile/Cristian Enache3
Citizenship: Canadian, Romanian
Education
2005 Ph.D. Mathematics, Laval University, Qu´ebec (advisor: Prof. G´erard A. Philippin)
2002 M.Sc. Mathematics, Laval University, Qu´ebec (advisor: Prof. G´erard A. Philippin)
2000 M.Sc. Mathematics, Ovidius University of Constanta (advisor: Prof. Constantin Varsan)
1999 B.Sc. Mathematics & Computer Science, Ovidius University of Constanta
Professional History
2013 – 2015 CNCS Researcher, Institute of Mathematics of the Romanian Academy
2014 – 2015 Assistant Professor, American University of the Middle East (affiliated with Purdue U.)
2013 – 2013 BITDEFENDER Researcher, Institute of Mathematics of the Romanian Academy
2010 – 2013 POSDRU Researcher, Ovidius University of Constanta
2009 – 2012 Assistant Professor, Ovidius University of Constanta
2008 – 2010 CNCSIS Researcher, Ovidius University of Constanta
2008 – 2008 NSERC-JSPS Researcher, Hiroshima University
2006 – 2008 NSERC-JSPS Researcher, Ehime University
2003 – 2005 Lecturer, Laval University
2000 – 2005 Teaching Assistant, Laval University
1999 – 2000 Teaching Assistant, Ovidius University of Constanta
Short-term visiting positions
2016 30.01 - 30.03 Tohoku University, Sendai, Japan (Prof. Shigeru Sakaguchi)
2015 15.08 - 23.11 Laval University, Qu´ebec, Canada (Prof. G´erard A. Philippin)
2013 24.03 - 27.05 Laval University, Qu´ebec, Canada (Prof. G´erard A. Philippin)
2012 01.10 - 30.11 University of Cologne, Cologne, Germany (Prof. Bernd Kawohl)
01.03 - 30.04 University of Florence, Florence, Italy (Prof. Paolo Salani)
2011 15.09 - 10.12 University of Science and Technology of China, Hefei, China (Prof. Xi-Nan Ma)
23.07 - 15.08 Laval University, Qu´ebec, Canada (Prof. G´erard A. Philippin)
2010 13.10 - 27.10 Lisbon University, Lisbon, Portugal (Prof. Pedro Freitas)
05.11 - 30.10 Lisbon University, Lisbon, Portugal (Prof. Pedro Freitas)
19.08 - 29.09 Hiroshima University, Higashi-Hiroshima, Japan (Prof. Shigeru Sakaguchi)
2009 21.11 - 05.12 Elie Cartan Institute, Nancy, France (Prof. Antoine Henrot)
05.11 - 20.11 Savoie University, Chambery, France (Prof. Dorin Bucur)
01.10 - 31.10 Pontifica Universidad Catolica de Chile, Santiago, Chile (Prof. Rafel Benguria)
01.09 - 30.09 Laval University, Qu´ebec, Canada (Prof. G´erard A. Philippin)
22.03 - 06.04 Laval University, Qu´ebec, Canada (Prof. G´erard A. Philippin)
08.03 - 21.03 Cornell University, Ithaca, USA (Prof. Lawrence E. Payne)
26.02 - 07.03 Laval University, Qu´ebec, Canada (Prof. G´erard A. Philippin)
Research interests
Partial Differential Equations, Mathematical Physics, Applicable Analysis and Geometric Analysis

2. CRISTIAN ENACHE CURRICULUM VITAE 2
Awards, Honors, Research Funding
2013 – 2015 CNCS Research Grant PN-II-ID-PCE-2012, Romania
2013 – 2013 BITDEFENDER PD Fellowship, Romania
2010 – 2013 POSDRU Research Fellowship 89/1.5/S/58852, Romania
2008 – 2010 CNCSIS Research Grant PN-II-RU-RP-2008, Romania
2006 – 2008 JSPS Grant-in-Aid for Scientific Research, Japan
2006 – 2008 NSERC-JSPS Postdoctoral Fellowship, Japan
2006 – 2008 NSERC Visiting/Industrial R&D Fellowship, Canada [declined]
2003 – 2004 CRM Research and Travel bursary, Canada
2000 – 2004 ISM Distinguished Doctoral Fellowship (4 times), Canada
Publications
Peer-reviewed articles
19. (with Luminita Barbu) Some maximum principles for a general class of quasilinear anisotropic
equations and applications, Advances in Nonlinear Analysis, to appear.
18. (with Luminita Barbu) A Liouville type theorem for a class of anisotropic equations, Analele
Stiintifice ale Universitatii Ovidius Constanta Seria Matematica, to appear.
17. Necessary conditions of solvability and isoperimetric estimates for some Monge-Amp`ere problems
in the plane, Proceedings of the American Mathematical Society 143(1) (2015), 309-315.
16. (with G´erard A. Philippin) On some isoperimetric inequalities involving eigenvalues of symmetric
free membranes, Zeitschrift fuer Angewandte Mathematik und Mechanik 95(4) (2015), 424-430.
15. (with Gerard A. Philippin) On some isoperimetric inequalities involving eigenvalues of fixed mem-
branes, Applied Mathematics Letter, 50 (2015), 10-15.
14. A note on a Liouville type theorem for p-Laplace equations, Electronic Journal of Differential
Equations 182 (2015), 1-7.
13. Maximum and minimum principles for a class of Monge-Amp`ere equations in the plane, with ap-
plications to surfaces of constant Gauss curvature, Communications on Pure and Applied Analysis
13(3) (2014), 1347-1359.
12. Maximum principles and isoperimetric inequalities for some Monge-Amp`ere type problems, Comptes
Rendus de l’Acadmie des Sciences Paris Series I - Mathematics 352 (2014), 37-42.
11. (with G´erard A. Philippin) Some inequalities involving eigenvalues of the Neumann Laplacian,
Mathematical Methods in the Applied Sciences 36 (2013), 2145-2153.
10. (with Luminita Barbu) A maximum principle for some fully nonlinear elliptic equations with
applications to Weingarten hypersurfaces, Complex Variables and Elliptic Equations 58 (2013),
1725-1736.
9. (with Luminita Barbu) A minimum principle for a soap film problem in R2, Zeitschrift fuer
angewandte Mathematik und Physik 64 (2013), 321-328.
8. (with Shigeru Sakaguchi) Some fully nonlinear elliptic boundary value problems with ellipsoidal
free boundaries, Mathematische Nachrichten 284 (2011), 1872-1879.
7. Lower bounds for blow-up time in some nonlinear parabolic problems under Neumann boundary
conditions, Glasgow Mathematical Journal 53 (2011), 569-575.
6. Blow-up phenomena for a class of quasilinear parabolic problems under Robin boundary condition,
Applied Mathematics Letters 24 (2011), 288-292.
5. Maximum principles and symmetry results for a class of fully nonlinear elliptic PDEs, NODEA
Nonlinear Differential Equations and Applications 17(5) (2010), 591-600.

3. CRISTIAN ENACHE CURRICULUM VITAE 3
4. Blow-up, global existence and exponential decay estimates for a class of quasilinear parabolic
problems, Nonlinear Analysis: Theory, Methods & Applications 69 (2008), 2864-2874.
3. Spatial decay bounds and continuous dependence on the data for a class of parabolic initial-
boundary value problems, Journal of Mathematical Analysis and Applications 323 (2006), 993-
1000.
2. Some maximum principles for a class of elliptic boundary value problems, Mathematical Inequal-
ities and Applications 9(4) (2006), 695-706.
1. Maximum Principles for a Class of Nonlinear Second-Order Elliptic Boundary Value Problems
in Divergence Form, Boundary Value Problems (2006), 13p.
Submitted papers/Preprints
3. (with Josep Batle, Mahmoud Abdel-Aty, Choon-Lin Ho) Optimal effective mass distribution m(z)
for a particle in 1D and 2D heterojunctions, submitted to Physical Review A.
2. (with Rafael Lopez) Maximum and minimum principles for some prescribed mean curvature
equations, preprint.
1. Some Liouville type theorems for a class of Monge-Amp`ere equations, preprint
Drafts/Works in progress
6. On the hot spot conjecture of J. Rauch.
5. On the Pompeiu-Schiffer conjecture.
4. (with Shigeru Sakaguchi) Pseudo-hessian equations: Existence, Regularity, Concavity.
3. A Cauchy-Liouville type theorem for fourth-order elliptic equations.
2. (with Luminita Barbu) A necessary condition of solvability for a free soap film problem.
1. On some convexity results for a general class of mean curvature type equations, draft
Conference talks
2015 Oct. Maximum principles and isoperimetric estimates for a class of Monge-Amp`ere equations, with
applications to surfaces of constant Gauss curvature
AMS Central Fall Sectional Meeting, Chicago, USA
June Maximum and minimum principles for a class of Monge-Amp`ere equations, with applications
to surfaces of constant Gauss curvature
CMS Summer Meeting, Charlottetown, Canada
2014 Aug. Maximum and minimum principles for a class of Monge-Amp`ere equations in the plane, with
applications to surfaces of constant Gauss curvature
XII-`eme Colloque Franco-Roumain de Maths Appliqu´ees, Univ. of Lyon, France
2013 June On some convexity results for mean curvature type equations
Joint International Meeting of the AMS and the RMS, Alba-Iulia, Romania
2012 Aug. Principes du minimum et estimations g´eom´etriques pour certains probl`emes de capillarit´e
XI-`eme Colloque Franco-Roumain de Maths Appliqu´ees, Univ. of Bucharest, Romania
June Some fully nonlinear elliptic boundary value problems with ellipsoidal free boundaries
New Trends in Shape Optimization, CRM Ennio DeGiorgi, Italy
June Minimum principles and geometric a priori bounds for some capillary problems in the plane
Workshop on Geometry of Interfaces and Capillarity, Granada Univ., Spain
2011 Nov. On some inequalities involving eigenvalues of the Neumann Laplacian
The Yangtze River Delta Conference on PDE’s, Ning Bo Univ., China
Jul. On some bounds estimates for means of low eigenvalues of the Neumann Laplacian
7th Congress of Romanian Mathematician, Transilvania Univ., Romania

4. CRISTIAN ENACHE CURRICULUM VITAE 4
2010 Aug. Bounds on the product of low eigenvalues of the Neumann Laplacian
13th Hiroshima Applied Math. Seminar, Hiroshima Univ., Japan
2008 Sep. Maximum principles and symmetry results for a class of fully nonlinear elliptic PDE’s
9th Hiroshima Applied Analysis Seminar, Hiroshima Univ., Japan
2005 July Some a priori bounds for the Poisson equation on riemannian manifolds
Int. Workshop on Differential Equations and Dynamical Systems, Guelph Univ., Canada
June Decay bounds and continuity results for a semilinear diffusion equation
Canadian Mathematical Society Summer Meeting, Waterloo Univ., Canada
May On the spectrum of the Riemannian manifolds
ISM-Wide Graduate Student Conference, UQAM, Canada
2004 Aug. Continuous dependence on the initial data for a heat equation in a long cylindrical region
Int. Conf. on Nonl. Operators, Diff. Eqs and Applications, Babes-Bolyai Univ., Romania
June Some a priori bounds for a class of nonlinear elliptic problems
Canadian Mathematical Society Summer Meeting, Dalhousie Univ., Canada
Apr. On some a priori bounds for Poisson equation
ISM-Wide Graduate Student Conference, Montreal Univ., Canada
2003 Apr. Maximum principles and symmetry for some nonlinear elliptic equations
ISM-Wide Graduate Student Conference, Laval Univ., Canada
Seminar talks
2015 Now. Maximum principles and some applications to surfaces of constant Gauss curvature
Univ. of Ottawa Seminar, Ottawa, Canada
Sep. Maximum principles and some applications to surfaces of constant Gauss curvature
Laval Univ. Seminar, Quebec, Canada
Mar. On some applications of the maximum principles in geometry and physics
American Univ. of the Middle East Seminar, Egailla, Kuwait
2013 Oct. Maximum principles, symmetry results and isoperimetric inequalities for some fully nonlinear
problems, with applications to the theory of surfaces of constant gaussian/scalar curvature
Ovidius Univ. Seminar, Constanta, Romania
May On some convexity results for mean curvature type equations
Ovidius Univ. Seminar, Constanta, Romania
2012 Oct. A short survey on P-functions and their applications
Univ. of Cologne Seminar, Cologne, Germany
May Problems with free boundaries. Bernoulli problems
Ovidius Univ. Seminar, Constanta, Romania
Apr. On some inequalities involving eigenvalues of the Neumann Laplacian
Florence Univ. Seminar, Florence, Italy
Apr. Maximum principles and their applications to the study of physical and geometrical problems
Florence Univ. Seminar, Florence, Italy
Jan. On some classes of hypersurfaces of prescribed curvatures
Ovidius Univ. Seminar, Constanta, Romania
2011 Mar. On some blow-up phenomena in parabolic problems
Ovidius Univ. Seminar, Constanta, Romania
2010 Dec. Uniqueness of the critical points of the solutions to some capillary problems in R2
Ovidius Univ. Seminar, Constanta, Romania
Nov. Some fully nonlinear elliptic boundary value problems with ellipsoidal free boundaries
Lisbon Univ. Seminar, Lisbon, Portugal
Mar. On some elements of Geometric Analysis of Mathematical Physics Equations
Ovidius Univ. Seminar, Constanta, Romania

5. CRISTIAN ENACHE CURRICULUM VITAE 5
2009 Nov. In´egalit´es isop´erimetriques pour les valeurs propres du Laplacian-Neumann
Univ. de Savoie Seminar, Chambery, France
Oct. Bounds on the product of the first two non-trivial frequencies of a free membrane
Pontifical Catholic Univ. of Chile Seminar, Santiago, Chile
Oct. Some fully nonlinear elliptic boundary value problems with ellipsoidal free boundaries
Pontifical Catholic Univ. of Chile Seminar, Santiago, Chile
Sep. Quelques probl`emes elliptiques compl`etement non-lin´eaires `a fronti`ere libre ellipsoidale
Laval Univ. Seminar, Quebec, Canada
Feb. Spectral Geometry in Mathematical Physics. Isoperimetric Inequalities
Ovidius Univ. Seminar, Constanta, Romania
Jan. Some fully nonlinear elliptic problems with ellipsoidal free boundaries
Ovidius Univ. Seminar, Constanta, Romania
2008 Apr. On some fully nonlinear overdetermined problems with ellipsoidal free boundaries
Hiroshima Univ. Seminar, Hiroshima, Japan
2006 Nov. Some applications of the maximum principles to the study of the PDE’s properties
Ehime Univ. Seminar, Matsuyama, Japan
2005 June Some maximum principles and applications to elliptic and parabolic problems
Bishop Univ. Seminar, Lennoxville, Canada
2002 Feb. On positive harmonic functions
Laval Univ. Seminar, Quebec, Canada
Other participations in international workshops/conferences
2012 July Geometric inequalities in Calculus of Variations, CRM Ennio DeGiorgi, Italy
May Shape optimization problems and spectral theory, CIRM Marseille, France
May Workshop for Young Researchers in Mathematics (2nd edition), Ovidius Univ., Romania
2011 Sep. USTC/NUS Mathematical Workshop, Univ. of Science and Technology of China, China
Aug. The 10th Intl Workshop on Diff. Geometry and its Applications, Ovidius Univ., Romania
Jul. Geometric properties of solutions of nonlinear PDEs and their applications, BIRS, Canada
July 7th Congress of Romanian Mathematician, Transilvania Univ., Romania
May Workshop for Young Researchers in Mathematics (1st edition), Ovidius Univ., Romania
2009 Nov. Journ´ees EDP Rhˆone-Alpes-Auvergne (7-i´eme edition), Inst. Fourier Grenoble, France
2008 Sep. 3rd Euro-Japanese Workshop on Blow-up, Tohoku Univ., Japan
Sep. 9th Hiroshima Applied Analysis Seminar, Hiroshim Univ., Japan
Aug. The 33rd Sapporo Symposium on Partial Differential Equations, Hokkaido Univ., Japan
June Problems in the Calculus of Variations and Related Topics, RIMS Kyoto, Japan
June Viscosity solutions of differential equations and Related Topics, RIMS Kyoto, Japan
Feb. 8th Matsuyama Analysis Seminar, Ehime Univ., Japan
2007 Dec. Recent Advances in Nonlinear Parabolic and Elliptic Diff. Eqns., Ryukoku Univ., Japan
June Int. Conference for the 25th Anniversary of Viscosity Solutions, Tokyo Univ., Japan
Feb. Workshop on Inverse Problems, Tsukuba Univ., Japan
Feb. 7th Matsuyama Analysis Seminar, Ehime Univ., Japan
2006 Oct. Recent Topics on Differential Equations, Gunma Univ., Japan
2004 Dec. Canadian Mathematical Society Winter Meeting, McGill Univ., Canada
Aug. Workshop on Spectral Theory of Schrodinger Operators, CRM Montreal, Canada
June Workshop on Semi-classical Theory of Eigenfunctions and PDE’s II, Fields Institute, Canada
June Workshop on Semi-classical Theory of Eigenfunctions and PDE’s I, CRM Montreal, Canada
Mar. Workshop on Spectral Geometry, CRM, Canada
2003 Oct. Conference on Classical Analysis in honor of Paul Koosis, CRM Montreal, Canada
2001 Sep. 4th Operator Algebras and Mathematical Physics Int. Conf., Ovidius Univ., Romania
1999 Aug. 7th Conf. on Nonl. Anal., Num. Anal., Appl. Math. and Inf., Ovidius Univ. Romania
July Summer School in Nonlinear Analysis, Transilvania Univ., Romania

6. CRISTIAN ENACHE CURRICULUM VITAE 6
Organizing activities (workshops/conferences)
2015 May Organizer of Workshop for Young Researchers in Mathematics (5th edition), Ovidius
Univ., Constanta, Romania
2014 May Organizer of Workshop for Young Researchers in Mathematics (4th edition), Ovidius
Univ., Constanta, Romania
2013 May Organizer of Workshop for Young Researchers in Mathematics (3rd edition), Ovidius
Univ., Constanta, Romania
2012 May Organizer of Workshop for Young Researchers in Mathematics (2nd edition), Ovidius
Univ., Constanta, Romania
2011 May Organizer of Workshop for Young Researchers in Mathematics, (1st edition), Ovidius
Univ., Constanta, Romania
Referee and review activities
Abstract and Applied Analysis
Analele Universitatii Ovidius din Constanta
Applicable Analysis
Applied Mathematics & Computations
Applied Mathematics Letters
Boundary Value Problems
Computers and Mathematics with Applications
Differential Equations and Applications
Discrete and Continuous Dynamical Systems - Series S (DCDS-S)
Electronic Journal of Differential Equations
Journal of Mathematical Analysis and Applications
Mathematical Review
Zeitschrift fuer Angewandte Mathematik und Physik (ZAMP)
Memberships
American Mathematical Society
Canadian Mathematical Society
”Japan Society for the Promotion of Science” Alumni Romania
Teaching activities
Courses taught at American University of the Middle East (Kuwait)
2015 Sum. Multivariate Calculus [15 hours/week; 2 sections]
Basic Mathematics [7.5 hours/week; 1 section]
Spr. Geometry and Calculus I [6 hours/week; 2 sections]
Multivariate Calculus [12 hours/week; 4 sections]
2014 Fall Geometry and Calculus I [9 hours/week; 3 sections]
Multivariate Calculus [6+2 hours/week; 2 sections]
Sum. Multivariate Calculus [20 hours/week; 2 sections]
Spr. Geometry and Calculus I [15 hours/week; 5 sections]
Courses taught at Univ. of Science and Technology of China (China)
2011 Fall Maximum principles and their applications [2.5 hours/lecture/week]
Courses taught at Ovidius Univ. (Romania)
2013 Spr. Convexity and starshapedness in PDE’s [2 hours/lecture/week]
2011 Spr. Liouville-Type Theorems for Elliptic Problems [2 hours/lecture/week]

7. CRISTIAN ENACHE CURRICULUM VITAE 7
2010 Spr. Brunn-Minkowski Inequalities in Geometry and Mathematical Physics [2 hours/lecture/week]
2009 Fall Introduction in the Theory of Stochastic Differential Equations [2 hours/lecture/week]
Spr. Spectral Geometry in Mathematical Physics [2 hours/lecture/week]
Courses taught at Laval Univ. (Canada)
2004 Fall Mathematics for Engineers III [3 hours/lecture/week]
2004 Sum. Mathematics for Engineers III [3 hours/lecture/week]
2003 Sum. Mathematics for Engineers III [3 hours/lecture/week]
Recitations led at Laval Univ. (Canada)
2000 – 2005 Mathematics for Engineers I, II and III, Mathematics for Scientists, Numerical Analysis
for Engineers, Classical Algebra, Introduction in Linear Algebra, Geometry for Primary
School Education Teching
Recitations led at Ovidius Univ. (Romania)
1999 – 2000 Ordinary Differential Equations, Integral Equations, Mathematics for Engineers I and
II, Mathematics for Scientists
Special teaching activities
2000 – 2005 Instructor at Centre de d´epannage et d’apprentissage en math´ematiques et statistique
(CDA), Univ. Laval, Qu´ebec, Canada
References
G´erard A. PHILIPPIN (MSc&PhD advisor)
Department of Mathematics and Statistics
Laval University
Qu´ebec, G1V 0A6, Canada
gphilip@mat.ulaval.ca
Xi-Nan MA
Department of Mathematics
University of Science and Technology of China
Hefei, 230 026, China
xinan@ustc.edu.cn
Antoine HENROT
l’Institut Elie Cartan
Universiote de Lorraine
54506 Vandoeuvre-ls-Nancy Cedex, France
antoine.henrot@univ-lorraine.fr
Armen BAGDASARYAN (teaching)
Department of Mathematics and Statistics
American University of the Middle East
Block 3, Al-Eqaila, Kuwait
bagdasari@yahoo.com
Shigeru SAKAGUCHI (PD advisor)
Graduate School of Information Sciences
Tohoku University
Sendai, 980-8579, Japan
sigersak@m.tohoku.ac.jp
Bernd KAWOHL
Mathematical Institute
University of Cologne
Cologne, 50923, Germany
kawohl@math.uni-koeln.de
Mihai MIHAILESCU
Department of Mathematics
University of Craiova
Craiova, 200585 , Romania
mmihailes@yahoo.com
Paolo SALANI
Department of Mathematics
University of Florence
Florence, 50134, Italy
paolo.salani@unifi.it