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arXiv · 0910.2015

The Extension for Mean Curvature Flow with Finite Integral Curvature in Riemannian Manifolds

Hong-Wei Xu·Fei Ye·En-Tao Zhao
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Abstract

We investigate the integral conditions to extend the mean curvature flow in a Riemannian manifold. We prove that the mean curvature flow solution with finite total mean curvature on a finite time interval $[0,T)$ can be extended over time $T$. Moreover, we show that the condition is optimal in some sense.

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Hong-Wei Xu, Fei Ye, En-Tao Zhao. 2009-10-11. The Extension for Mean Curvature Flow with Finite Integral Curvature in Riemannian Manifolds. https://arxiv.org/abs/0910.2015

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