Gauss curvature flow with shrinking obstacle

被引：0

作者：

Lee, Ki-Ahm ^{[1
,2
]}

Lee, Taehun ^{[3
]}

机构：

[1] Seoul Natl Univ, Dept Math Sci, Seoul 08826, South Korea

[2] Seoul Natl Univ, Res Inst Math, Seoul 08826, South Korea

[3] Korea Inst Adv Study, Sch Math, Seoul 02455, South Korea

来源：

MATHEMATISCHE ANNALEN | 2024年 / 389卷 / 04期

关键词：

FREE-BOUNDARY PROBLEMS; CONVEX HYPERSURFACES; GENERAL-CLASS; REGULARITY; SHAPES;

D O I：

10.1007/s00208-023-02739-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a flow by powers of Gauss curvature under the obstruction that the flow cannot penetrate a prescribed region, so called an obstacle. For all dimensions and positive powers, we prove the optimal curvature bounds of solutions and all time existence with its long time behavior. We also prove the C-1 regularity of free boundaries under a uniform thickness assumption.

引用

页码：4055 / 4082

页数：28

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