Non-scale-invariant inverse curvature flows in Euclidean space

被引：53

作者：

Gerhardt, Claus ^{[1
]}

机构：

[1] Heidelberg Univ, Inst Angew Math, D-69120 Heidelberg, Germany

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2014年 / 49卷 / 1-2期

关键词：

SURFACES; HYPERSURFACES; SPHERES;

D O I：

10.1007/s00526-012-0589-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the inverse curvature flows (x) over dot = F-p nu of closed star-shaped hypersurfaces in Euclidean space in case 0 < p not equal 1 and prove that the flow exists for all time and converges to infinity, if 0 < p < 1, while in case p > 1, the flow blows up in finite time, and where we assume the initial hypersurface to be strictly convex. In both cases the properly rescaled flows converge to the unit sphere.

引用

页码：471 / 489

页数：19

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