Iosif Polterovich

The Steklov problem inside out

The Steklov eigenvalue problem has been a central topic in spectral geometry over the past decade. In this talk, we introduce a new variation of the problem formulated in the exterior of a bounded domain rather than in its interior. We begin by presenting several natural ways to define the exterior Steklov problem, and then turn to inequalities for the first eigenvalue. Particular attention will be given to the contrasts between the interior and exterior settings, as well as to the differences arising in two dimensions versus higher dimensions. The talk is based on joint work with L. Bundrock,  A. Girouard, D. Grebenkov and M. Levitin.