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 at 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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Dedicated to Professor Buqing Su on his 110th Anniversary
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Xu, H., Ye, F. & Zhao, E. The extension for mean curvature flow with finite integral curvature in Riemannian manifolds. Sci. China Math. 54, 2195–2204 (2011). https://doi.org/10.1007/s11425-011-4244-3
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DOI: https://doi.org/10.1007/s11425-011-4244-3