The document discusses the Kneser-Poulsen conjecture regarding how the area of the union and intersection of discs changes when the distances between disc centers increases. It provides background on results proving the conjecture holds in certain spaces, including Euclidean space in 2D if there is continuous expansion. The challenges in extending these proofs to higher dimensions are discussed, as are analogous questions regarding spherical and hyperbolic spaces.

1. Problems related to the Kneser-Poulsen conjecture Maria Belk

2. A Bunch of Discs

23. Continuous Case Wall Why? Because  =     , where   = size of Wall between discs  and    = change in distance between   and      

24. Continuous Case Why? Because  =     , where   = size of Wall between discs  and    = change in distance between   and      

46. The problems of extending this proof to higher dimensions.

50. Another Example

57. Hyperbolic and Spherical Spaces

62. Tensegrities

83. Remaining Questions