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Session S33 - Spectral Geometry

Tuesday, July 13, 15:30 ~ 15:50 UTC-3

Eigenvalue bounds for the mixed Steklov problem in two dimensions

Emily Dryden

Bucknell University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The Steklov problem is an eigenvalue problem for manifolds with boundary; the eigenvalues can also be viewed as the eigenvalues of the Dirichlet-to-Neumann operator, or voltage-to-current map. The question of finding meaningful bounds for these eigenvalues has a long history, beginning with Weinstock's isoperimetric inequality for the lowest nontrivial Steklov eigenvalue of a simply-connected Lipschitz planar domain. We will explore some recent contributions to the story, with an emphasis on results that can be seen in pictures.

Joint work with Teresa Arias-Marco (Universidad de Extremadura, Spain), Carolyn S. Gordon (Dartmouth College, USA), Asma Hassannezhad (University of Bristol, UK), Allie Ray (Birmingham-Southern College, USA) and Elizabeth Stanhope (Lewis & Clark College, USA).

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