Spectral Invariants of the Magnetic Dirichlet-to-Neumann Map on Riemannian Manifolds

Abstract

This paper is devoted to investigate the heat trace asymptotic expansion corresponding to the magnetic Steklov eigenvalue problem on Riemannian manifolds with boundary. We establish an effective procedure, by which we can calculate all the coefficients $a_0$, $a_1$, $\dots$, $a_{n-1}$ of the heat trace asymptotic expansion. In particular, we explicitly give the expressions for the first four coefficients. These coefficients are spectral invariants which provide precise information concerning the volume and curvatures of the boundary of the manifold and some physical quantities by the magnetic Steklov eigenvalues.

26 pages. This is a new work for eigenvalues of the magnetic Steklov eigenvalue problem on Riemannian manifolds with boundary

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• On the asymptotic number of edge states for magnetic Schrödinger operators
• Determination of isometric real-analytic metric and spectral invariants for elastic Dirichlet-to-Neumann map on Riemannian manifolds
• Geometric invariants of spectrum of the Navier-Lamé operator