Harnack inequalities for evolving hypersurfaces on the sphere

被引：4

作者：

Bryan, Paul ^{[1
]}

Ivaki, Mohammad N. ^{[2
]}

Scheuer, Julian ^{[3
]}

机构：

[1] Macquarie Univ, Dept Math, N Ryde, NSW 2109, Australia

[2] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada

[3] Albert Ludwigs Univ, Math Inst, Ernst Zermelo Str 1, D-79104 Freiburg, Germany

来源：

COMMUNICATIONS IN ANALYSIS AND GEOMETRY | 2018年 / 26卷 / 05期

基金：

英国工程与自然科学研究理事会; 奥地利科学基金会; 欧洲研究理事会;

关键词：

CONVEX HYPERSURFACES; CURVATURE FLOWS;

D O I：

10.4310/CAG.2018.v26.n5.a2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove Harnack inequalities for hypersurfaces flowing on the unit sphere by p-powers of a strictly monotone, 1-homogeneous, convex, curvature function f, 0 < p <= 1. If f is the mean curvature, we obtain stronger Harnack inequalities.

引用

页码：1047 / 1077

页数：31

共 27 条

[1] HARNACK INEQUALITIES FOR EVOLVING HYPERSURFACES [J].

ANDREWS, B .

MATHEMATISCHE ZEITSCHRIFT, 1994, 217 (02) :179-197

[2] CONTRACTION OF CONVEX HYPERSURFACES IN EUCLIDEAN-SPACE [J].

ANDREWS, B .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 1994, 2 (02) :151-171

[3] Pinching estimates and motion of hypersurfaces by curvature functions [J].

Andrews, Ben .

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2007, 608 :17-33

[4] Contracting convex hypersurfaces by curvature [J].

Andrews, Ben ;

McCoy, James ;

Zheng, Yu .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2013, 47 (3-4) :611-665

[5] Moving surfaces by non-concave curvature functions [J].

Andrews, Ben .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2010, 39 (3-4) :649-657

[6]

Bryan P., 2015, ARXIV150802821

[7] Classification of Convex Ancient Solutions to Curve Shortening Flow on the Sphere [J].

Bryan, Paul ;

Louie, Janelle .

JOURNAL OF GEOMETRIC ANALYSIS, 2016, 26 (02) :858-872

[8] ON HARNACK INEQUALITY AND ENTROPY FOR THE GAUSSIAN CURVATURE FLOW [J].

CHOW, B .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1991, 44 (04) :469-483

[9] Space-time Formulation of Harnack Inequalities for Curvature Flows of Hypersurfaces [J].

Chow, Bennett ;

Chu, Sun-Chin .

JOURNAL OF GEOMETRIC ANALYSIS, 2001, 11 (02) :219-231

[10]

Gerhardt C., 2006, SERIES GEOMETRY TOPO, V39

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