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arXiv · 0806.1758

The harmonic mean curvature flow of nonconvex surfaces in $\mathbb{R}^3$

Panagiota Daskalopoulos·Natasa Sesum
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Abstract

We consider a compact, star-shaped, mean convex hypersurface $Σ^2\subset \mathbb{R}^3$. We prove that in some cases the flow exists until it shrinks to a point in a spherical manner, which is very typical for convex surfaces as well (see \cite{An1}). We also prove that in the case we have a surface of revolution which is star-shaped and mean convex, a smooth solution always exists up to some finite time $T < \infty$ at which the flow shrinks to a point asymptotically spherically.

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Panagiota Daskalopoulos, Natasa Sesum. 2008-09-03. The harmonic mean curvature flow of nonconvex surfaces in $\mathbb{R}^3$. https://arxiv.org/abs/0806.1758

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