Abstract
AbstractWe 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$$L^2$$L2-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.
Funder
Max Planck Institute for Mathematics
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Analysis
Reference25 articles.
1. Ballmann, W., Matthiesen, H., Polymerakis, P.: On the bottom of spectra under coverings. Math. Z. 288(3–4), 1029–1036 (2018)
2. Ballmann, W., Polymerakis, P.: Bottom of spectra and coverings. Surv. Differ. Geom. 23, 1–13 (2020)
3. Bessa, G.P., Montenegro, J.F., Piccione, P.: Riemannian submersions with discrete spectrum. J. Geom. Anal. 22(2), 603–620 (2012)
4. Bordoni M.: Spectra of submersions, Contemporary geometry and related topics, Univ. Belgrade Fac. Math., Belgrade, pp. 51–62, available at https://emis.de/proceedings/CGRT2005/ (2006)
5. Brooks, R.: The fundamental group and the spectrum of the Laplacian. Comment. Math. Helv. 56(4), 581–598 (1981)
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