Optimal regularity of plurisubharmonic envelopes on compact Hermitian manifolds

Abstract

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

14 pages; final version to appear in SCIENCE CHINA Mathematics

References in corpus (3)

• On the $C^{1,1}$ regularity of geodesics in the space of Kähler metrics
• Weak solutions of complex Hessian equations on compact Hermitian manifolds
• The parabolic Monge-Ampère equation on compact almost Hermitian manifolds

Cited by in corpus (1)

• Regularity of the plurisubharmonic envelope in strictly pseudoconvex domains