Non-scale-invariant inverse curvature flows in Euclidean space

Abstract

We consider the inverse curvature flows $\dot{x}=F^{-p}\nu$ of closed star-shaped hypersurfaces in Euclidean space in case $0<p\ne 1$ 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.

21 pages, this is the published version

References in corpus (2)

• Curvature flows in semi-Riemannian manifolds
• Surfaces expanding by the inverse Gauss curvature flow

Cited by in corpus (30)

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• The inverse mean curvature flow in warped cylinders of non-positive radial curvature
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• New pinching estimates for Inverse curvature flows in space forms
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• Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature
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• Flow by Gauss curvature to the Aleksandrov and dual Minkowski problems
• Strong spherical rigidity of ancient solutions of expansive curvature flows
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• A generalized Gauss curvature flow related to the Orlicz-Minkowski problem
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• Curvature bound for $L_p$ Minkowski problem
• The planar Busemann-Petty centroid inequality and its stability
• A Class Of Curvature Flows Expanded By Support Function And Curvature Function In The Euclidean Space And Hyperbolic Space
• A class of curvature flows expanded by support function and curvature function
• Inverse Gauss curvature flows with free boundaries in a cone
• A flow method for the dual Orlicz-Minkowski problem
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• A curvature flow approach to Lp-Christoffel-Minkowski problem for p>1
• Evolution of starshaped hypersurfaces by general curvature functions
• An application of dual convex bodies to the inverse Gauss curvature flow