|DATE:||Wednesday, March 19th|
|TIME:||4:30 PM - 5:30 PM|
|TITLE:||On the Kneser-Poulsen Conjecture for spheres|
|SPEAKER:||Robert Connelly, Mathematics Department, Cornell Univ.|
If a finite set of disks in the plane is rearranged so that the distance
between each pair of centers does not decrease, then the area of the union
does not decrease, and the area of the intersection does not increase.
This is the case, in the plane, of a conjecture by Kneser (1955) and
Poulsen (1954), recently proved by K. Bezdek and me. The analogous
question for disks on the 2-dimensional sphere, and for all
higher-dimensional spheres and higher-dimensional Euclidean space remains
open. I will show this conjecture for unit spheres for all dimensions,
but with the restriction that all the disks on the spheres are
hemispheres. This is joint work with K. Bezdek, and follows the same
general plan as in the plane, but is somewhat simpler.