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A pinching estimate for convex hypersurfaces evolving under a non-homogeneous variant of mean curvature flow

Part of: Partial differential equations

Published online by Cambridge University Press:  18 April 2022

Tim Espin
Tim Espin*
Affiliation:
School of Mathematics, Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh, EH9 3FD, UK ([email protected])
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Abstract

We study a variant of the mean curvature flow for closed, convex hypersurfaces where the normal velocity is a non-homogeneous function of the principal curvatures. We show that if the initial hypersurface satisfies a certain pinching condition, then this is preserved and the flow converges to a sphere under rescaling.

Keywords

convex hypersurfacesnon-homogeneous curvature flow

MSC classification

Secondary: 35B40: Asymptotic behavior of solutions
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 65 , Issue 2 , May 2022 , pp. 376 - 391
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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