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- W4289293894 abstract "We study the evolution of complete non-compact convex hypersurfaces in $mathbb{R}^{n+1}$ by the inverse mean curvature flow. We establish the long time existence of solutions and provide the characterization of the maximal time of existence in terms of the tangent cone at infinity of the initial hypersurface. Our proof is based on an a'priori pointwise estimate on the mean curvature of the solution from below in terms of the aperture of a supporting cone at infinity. The strict convexity of convex solutions is shown by means of viscosity solutions. Our methods also give an alternative proof of the result by Huisken and Ilmanen on compact star-shaped solutions, based on maximum principle argument." @default.
- W4289293894 created "2022-08-02" @default.
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- W4289293894 date "2018-11-12" @default.
- W4289293894 modified "2023-09-27" @default.
- W4289293894 title "Evolution of non-compact hypersurfaces by inverse mean curvature" @default.
- W4289293894 doi "https://doi.org/10.48550/arxiv.1811.04594" @default.
- W4289293894 hasPublicationYear "2018" @default.
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