On the Steklov spectrum of covering spaces and total spaces

DOI10.1007/S10455-023-09884-2arXiv2106.00986MaRDI QIDQ6369206

Publication date: 2 June 2021

Abstract: We show the existence of a natural Dirichlet-to-Neumann map on Riemannian manifolds with boundary and bounded geometry, such that the bottom of the Dirichlet spectrum is positive. This map regarded as a densely defined operator in the

L^{2}

-space of the boundary admits Friedrichs extension. We focus on the spectrum of this operator on covering spaces and total spaces of Riemannian principal bundles over compact manifolds.

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Global differential geometry (53C99)

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