Surfaces moving by powers of Gauss curvature

Ben Andrews; Xuzhong Chen

doi:10.4310/PAMQ.2012.v8.n4.a1

Surfaces moving by powers of Gauss curvature

Ben Andrews^*, Xuzhong Chen

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

23 Citations (Scopus)

Abstract

We prove that strictly convex surfaces moving by K^α/2 become spherical as they contract to points, provided α lies in the range [1; 2]. In the process we provide a natural candidate for a curvature pinching quantity for surfaces moving by arbitrary functions of curvature, by finding a quantity conserved by the reaction terms in the evolution of curvature.

Original language	English
Pages (from-to)	825-834
Number of pages	10
Journal	Pure and Applied Mathematics Quarterly
Volume	8
Issue number	4
DOIs	https://doi.org/10.4310/PAMQ.2012.v8.n4.a1
Publication status	Published - Oct 2012

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10.4310/PAMQ.2012.v8.n4.a1

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title = "Surfaces moving by powers of Gauss curvature",

abstract = "We prove that strictly convex surfaces moving by Kα/2 become spherical as they contract to points, provided α lies in the range [1; 2]. In the process we provide a natural candidate for a curvature pinching quantity for surfaces moving by arbitrary functions of curvature, by finding a quantity conserved by the reaction terms in the evolution of curvature.",

keywords = "Curvature estimate, Gauss curvature flow",

author = "Ben Andrews and Xuzhong Chen",

year = "2012",

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AU - Chen, Xuzhong

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N2 - We prove that strictly convex surfaces moving by Kα/2 become spherical as they contract to points, provided α lies in the range [1; 2]. In the process we provide a natural candidate for a curvature pinching quantity for surfaces moving by arbitrary functions of curvature, by finding a quantity conserved by the reaction terms in the evolution of curvature.

AB - We prove that strictly convex surfaces moving by Kα/2 become spherical as they contract to points, provided α lies in the range [1; 2]. In the process we provide a natural candidate for a curvature pinching quantity for surfaces moving by arbitrary functions of curvature, by finding a quantity conserved by the reaction terms in the evolution of curvature.

KW - Curvature estimate

KW - Gauss curvature flow

UR - https://www.scopus.com/pages/publications/84864482146

U2 - 10.4310/PAMQ.2012.v8.n4.a1

DO - 10.4310/PAMQ.2012.v8.n4.a1

M3 - Article

SN - 1558-8599

VL - 8

SP - 825

EP - 834

JO - Pure and Applied Mathematics Quarterly

JF - Pure and Applied Mathematics Quarterly

IS - 4

ER -

Surfaces moving by powers of Gauss curvature

Abstract

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