On the Yamabe constants of product manifolds
Chanyoung Sung
TL;DR
This paper develops a comparison theorem for Yamabe constants on warped product manifolds using fiberwise spherical symmetrization and establishes the existence of radially-symmetric Yamabe minimizers on product manifolds with round spheres.
Contribution
It introduces a new comparison theorem for Yamabe constants on warped products and proves the existence of symmetric minimizers on certain product manifolds.
Findings
Comparison theorem for Yamabe constants on warped products
Existence of radially-symmetric Yamabe minimizers
Application to manifolds with round sphere factors
Abstract
By using the fiberwise spherical symmetrization we give a comparison theorem of Yamabe constants on warped products and prove the existence of radially-symmetric Yamabe minimizers on Riemannian manifolds given by products with round spheres.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Geometric Analysis and Curvature Flows · Analytic and geometric function theory