Event

Talk
Inverse Spectral Problems for Dirichlet-to-Neumann operators
Prof. Dr. Carolyn Gordon (Dartmouth College)
20 Jun 2016, 14:30 – 15:30

The Dirichlet-to-Neumann operator of a compact Riemannian manifold M with boundary is an endomorphism of the space of smooth functions on the boundary that maps the Dirichlet boundary values of each harmonic function f on M to the Neumann boundary values of f. The spectrum of this operator is discrete and is called the Steklov spectrum. The Dirichlet-to-Neumann operator also generalizes to the setting of orbifolds. We will compare the behavior of the Steklov spectrum on smooth surfaces with that of two-dimensional orbifolds. In arbitrary dimensions, we will adapt techniques for constructing isospectral manifolds to the setting of the Steklov spectrum.

Related to:

• Carolyn S. Gordon
• [C2] Differential Geometry: Geometric and Spectral Invariants of Riemannian, Lorentzian and conformal manifolds