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

2021/08/17 by Liu, Genqian, Tan, Xiaoming · 1 citation
#35P20 #35S05 #58J40 #58J50 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2108.07611

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 a₀, a₁, …, 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.

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• Magnetic Steklov operator on differential forms

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