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arXiv · 2104.00047

$H^\alpha$-flow of mean convex, complete graphical hypersurfaces

Wolfgang Maurer
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Abstract

We consider the evolution of hypersurfaces in $\mathbb{R}^{n+1}$ with normal velocity given by a positive power of the mean curvature. The hypersurfaces under consideration are assumed to be strictly mean convex (positive mean curvature), complete, and given as the graph of a function. Long-time existence of the $H^{\alpha}$-flow is established by means of approximation by bounded problems.

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Wolfgang Maurer. 2021-03-31. $H^\alpha$-flow of mean convex, complete graphical hypersurfaces. https://arxiv.org/abs/2104.00047

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