|Location:||MSRI: Simons Auditorium|
Let D be a two-dimensional Riemannian disc. Denote its diameter by d,
its area by A, and the length of its boundary by L.
We demonstrate that the boundary of D can be contracted to a point
through closed curves of length less than 2d+4L+10000\sqrt(A) answering
an old question due to M. Gromov, S. Frankel and M. Katz. We are also going
to discuss several simply looking related problems that we do not know
how to solve. (Joint work with Y. Liokumovich and R. Rotman).