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Long time existence
of Yamabe flow on singular spaces with positive Yamabe
constant
Jørgen Olsen Lye and Boris Vertman |
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Vol. 16 (2023), No. 2, 477–510
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Abstract |
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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
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Mathematical Subject Classification
Primary: 35K08, 53E99, 58J35
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Milestones
Received: 2 June 2020
Revised: 7 April 2021
Accepted: 8 July 2021
Published: 3 May 2023
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Authors |
| Jørgen Olsen Lye | |
| Institut für
Differentialgeometrie Leibniz Universität Hannover Hannover Germany |
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| Boris Vertman | |
| Institut für Mathematik Universität Oldenburg Oldenburg Germany |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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