Optimal regularity of plurisubharmonic envelopes on compact Hermitian manifolds

Articles

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.

Keywords

complex Monge-Ampère equations plurisubharmonic functions envelopes Hermitian manifolds 

MSC(2010)

32W20 32U05 

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Notes

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 G. Tian for encouragement and support. After finishing writing this preprint, the authors learned that Theorem 1.1 in the case of Kähler manifolds is independently obtained by Tosatti [25] and solved a problem of Berman.

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesPeking UniversityBeijingChina

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