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Translating solitons of the mean curvature flow

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Abstract

We study some basic properties of translating solitons: the volume growth, generalized maximum principle, Gauss maps and certain functions related to the Gauss maps. Finally we carry out point-wise estimates and integral estimates for the squared norm of the second fundamental form. These estimates give rigidity theorems for translating solitons in the Euclidean space in higher codimension.

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Authors and Affiliations

  1. Institute of Mathematics, Fudan University, Shanghai, 200433, China

    Y. L. Xin

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

Additional information

Communicated by J. Jost.

The author is supported partially by NSFC.

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Xin, Y.L. Translating solitons of the mean curvature flow . Calc. Var. 54, 1995–2016 (2015). https://doi.org/10.1007/s00526-015-0853-y

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  • DOI: https://doi.org/10.1007/s00526-015-0853-y

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