Yamabe flow on manifolds with edges

Eric Bahuaud; Boris Vertman

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arXiv · 1107.5350

Yamabe flow on manifolds with edges

Eric Bahuaud·Boris Vertman

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Abstract

Let (M,g) be a compact oriented Riemannian manifold with an incomplete edge singularity. This article shows that it is possible to evolve g by the Yamabe flow within a class of singular edge metrics. As the main analytic step we establish parabolic Schauder-type estimates for the heat operator on certain Hölder spaces adapted to the singular edge geometry. We apply these estimates to obtain local existence for a variety of quasilinear equations, including the Yamabe flow. This provides a setup for a subsequent discussion of the Yamabe problem using flow techniques in the singular setting.

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Eric Bahuaud, Boris Vertman. 2013-07-13. Yamabe flow on manifolds with edges. https://arxiv.org/abs/1107.5350

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