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Optimal regularity of plurisubharmonic envelopes on compact Hermitian manifolds

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Abstract

In this paper, we prove the C1,1-regularity of the plurisubharmonic envelope of a C1,1 function on a compact Hermitian manifold. We also present the examples to show this regularity is sharp.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11571018 and 11331001). The first author would like to thank his advisor Professor G. Tian for encouragement and support. After finishing writing this preprint, the authors learned that Theorem 1.1 in the case of Kähler manifolds was independently obtained by Tosatti [25].

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Authors and Affiliations

  1. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Jianchun Chu & Bin Zhou

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  1. Jianchun Chu
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  2. Bin Zhou
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Correspondence to Bin Zhou.

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Chu, J., Zhou, B. Optimal regularity of plurisubharmonic envelopes on compact Hermitian manifolds. Sci. China Math. 62, 371–380 (2019). https://doi.org/10.1007/s11425-017-9173-0

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