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.
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页数：27
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