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

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

2009-10-11

arxiv.org/abs/0910.2015v1

Mathematics

Differential Geometry

13 pages

Scientific paper

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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