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Non-collapsing in homogeneity greater than one via a two-point method for a special case

Part of: Partial differential equations on manifolds; differential operators Partial differential equations Global differential geometry

Published online by Cambridge University Press:  24 January 2019

Heiko Kröner
Heiko Kröner*
Affiliation:
University of Hamburg, Department of Mathematics, Bundesstraße 55, 20146 Hamburg, Germany ([email protected])
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Abstract

We study the mechanism of proving non-collapsing in the context of extrinsic curvature flows via the maximum principle in combination with a suitable two-point function in homogeneity greater than one. Our paper serves as the first step in this direction and we consider the case of a curve which is C2-close to a circle initially and which flows by a power greater than one of the curvature along its normal vector.

Keywords

geometric evolution equationmaximum principle

MSC classification

Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
Secondary: 58J35: Heat and other parabolic equation methods 35B50: Maximum principles
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 6 , December 2019 , pp. 1627 - 1635
Copyright
Copyright © Royal Society of Edinburgh 2019 

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