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Long time existence of Yamabe flow on singular spaces with positive Yamabe constant

Jørgen Olsen Lye and Boris Vertman

Vol. 16 (2023), No. 2, 477–510
Abstract

We establish long-time existence of the normalized Yamabe flow with positive Yamabe constant on a class of manifolds that includes spaces with incomplete cone-edge singularities. We formulate our results axiomatically so that they extend to general stratified spaces as well, provided certain parabolic Schauder estimates hold. The central analytic tool is a parabolic Moser iteration, which yields uniform upper and lower bounds on both the solution and the scalar curvature.

Keywords
geometric evolution equations, Yamabe flow, positive scalar curvature, singular spaces, nonlinear parabolic equations
Mathematical Subject Classification
Primary: 35K08, 53E99, 58J35
Milestones
Received: 2 June 2020
Revised: 7 April 2021
Accepted: 8 July 2021
Published: 3 May 2023
Authors
Jørgen Olsen Lye
Institut für Differentialgeometrie
Leibniz Universität Hannover
Hannover
Germany
Boris Vertman
Institut für Mathematik
Universität Oldenburg
Oldenburg
Germany

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