Heat Invariants of the Steklov Problem

By Iosif Polterovich, David A. Sher. 2013

50 citations recorded by the source corpus.

We study the heat trace asymptotics associated with the Steklov eigenvalue problem on a Riemannian manifold with boundary. In particular, we describe the structure of the Steklov heat invariants and compute the first few of them explicitly in terms of the scalar and mean curvatures. This is done by applying the Seeley calculus to the Dirichlet-to-Neumann operator, whose spectrum coincides with the Steklov eigenvalues. As an application, it is proved that a three-dimensional ball is uniquely defined by its Steklov spectrum among all Euclidean domains with smooth connected boundary.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e9d016f6ce5f225480c7426608df017bd27c2a58

Citations in the corpus

• SPECTRAL GEOMETRY OF THE STEKLOV PROBLEM (2014, unknown): “This result was obtained in [90], and we sketch its proof below.”