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Curvature estimates for minimal submanifolds of higher codimension

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Abstract

The authors derive curvature estimates for minimal submanifolds in Euclidean space for arbitrary dimension and codimension via Gauss map. Thus, Schoen-Simon-Yau’s results and Ecker-Huisken’s results are generalized to higher codimension. In this way, Hildebrandt-Jost-Widman’s result for the Bernstein type theorem is improved.

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Authors and Affiliations

  1. Key Laboratory of Mathematics for Nonlinear Sciences, School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Yuanlong Xin

  2. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Ling Yang

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  1. Yuanlong Xin
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  2. Ling Yang
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Correspondence to Yuanlong Xin.

Additional information

Project supported by the National Natural Science Foundation of China (No. 10531090) and the Natural Science Foundation of the Ministry of Education of China.

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Xin, Y., Yang, L. Curvature estimates for minimal submanifolds of higher codimension. Chin. Ann. Math. Ser. B 30, 379–396 (2009). https://doi.org/10.1007/s11401-008-0438-6

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  • DOI: https://doi.org/10.1007/s11401-008-0438-6

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