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Mean Curvature Flow with Bounded Gauss Image

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Abstract

We study the mean curvature flow of a complete space-like submanifold in pseudo-Euclidean space with bounded Gauss image and bounded curvature. We establish a relevant maximum principle for our setting. Then, we can obtain the “confinable property” of the Gauss images and curvature estimates under the mean curvature flow. Thus we prove a corresponding long time existence result.

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Authors and Affiliations

  1. Institute of Mathematics, Fudan University, Shanghai, 200433, People’s Republic of China

    Y. L. Xin

  2. Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Education, Shanghai, People’s Republic of China

    Y. L. Xin

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  1. Y. L. Xin
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Correspondence to Y. L. Xin.

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Dedicated to Professor Heinrich Wefelscheid on his 70th birthday

The research was partially supported by NSFC.

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Xin, Y.L. Mean Curvature Flow with Bounded Gauss Image. Results. Math. 59, 415–436 (2011). https://doi.org/10.1007/s00025-011-0112-2

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  • DOI: https://doi.org/10.1007/s00025-011-0112-2

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