Flow by powers of the Gauss curvature in space forms

被引：1

作者：

Chen, Min ^{[1
]}

Huang, Jiuzhou ^{[2
]}

机构：

[1] 1203 Burnside Hall,805 Sherbrooke St West, Montreal, PQ H3A 0B9, Canada

[2] 1030 Burnside Hall, 805 Sherbrooke St West, Montreal, PQ H3A 0B9, Canada

来源：

ADVANCES IN MATHEMATICS | 2024年 / 442卷

基金：

中国国家自然科学基金;

关键词：

Entropy; Gauss curvature; Monotonicity; Regularity estimates; Space forms; CONVEX HYPERSURFACES; CONTRACTION; SURFACES; ENTROPY; SHAPES;

D O I：

10.1016/j.aim.2024.109579

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove that convex hypersurfaces under the flow by powers alpha > 0 of the Gauss curvature in space forms Nn+1 (K) of constant sectional curvature K (K = +/- 1) contract to a point in finite time T & lowast;. Moreover, convex hypersurfaces under the flow by power alpha > 1/n+2 curvature converge (after rescaling) to a limit which is the geodesic sphere in Nn+1 (K). This extends the known results in Euclidean space to space forms. (c) 2024 Elsevier Inc. All rights reserved.

引用

页数：27

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