Abstract
AbstractFor Riemannian submersions, we establish some estimates for the spectrum of the total space in terms of the spectrum of the base space and the geometry of the fibers. In particular, for Riemannian submersions of complete manifolds with closed fibers of bounded mean curvature, we show that the spectrum of the base space is discrete if and only if the spectrum of the total space is discrete.
Funder
Max Planck Institute for Mathematics
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Analysis
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