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A Note about Minimal Hypercones

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Abstract

This short note is concerned with a measure version criterion for hypersurfaces to be minimal. Certain natural flows and associated reflections for many minimal hypercones, including minimal isoparametric hypercones and area-minimizing hypercones, are studied.

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Acknowledgements

The author would like to thank Professors J. Y. Choe and J. Hoppe for drawing his attention to reference [1], the editor and anonymous referee for helpful comments, and IHES and MPIM for warm hospitalities where part of the work was conducted during the author’s visits.

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Authors and Affiliations

  1. School of Mathematical Sciences & IAS, Tongji University, Shanghai, 200092, P. R. China

    Yong Sheng Zhang

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  1. Yong Sheng Zhang
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Correspondence to Yong Sheng Zhang.

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Supported by NSFC (Grant Nos. 11971352, 11601071), the S. S. Chern Foundation through IHES and a Start-up Research Fund from Tongji University

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Zhang, Y.S. A Note about Minimal Hypercones. Acta. Math. Sin.-English Ser. 37, 1794–1802 (2021). https://doi.org/10.1007/s10114-020-0061-3

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  • DOI: https://doi.org/10.1007/s10114-020-0061-3

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