Fiberwise symmetrizations for variational problems on fibred manifolds

2021/08/28 by Sung, Chanyoung · 2 citations
#35P15 #49R05 #58E99 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2108.12651

Abstract

We establish a framework for fiberwise symmetrization to find a lower bound of a Dirichlet-type energy functional in a variational problem on a fibred Riemannian manifold, and use it to prove a comparison theorem of the first eigenvalue of the Laplacian on a warped product manifold.

Cited by

• On the Yamabe constants of product manifolds
• Volume spectrum of fiber bundles and the widths of Berger spheres

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