Regularity of the plurisubharmonic envelope in strictly pseudoconvex domains

2017/03/22 by Dinew, Slawomir
#Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1703.07727

Abstract

We study the plurisubharmonic envelopes of functions in the setting of domains in \mathbb Cⁿ. In particular we prove a complex analogue of a result of De Philippis and Figalli concerning the optimal regularity of such envelopes in smooth strictly pseudoconvex domains.

Related

• On plurisubharmonic defining functions for pseudoconvex domains in ℂ²
• Optimal regularity of plurisubharmonic envelopes on compact Hermitian manifolds
• On the conditional plurisubharmonic envelopes of bounded functions
• Rooftop envelopes and residual plurisubharmonic functions
• On smoothing of plurisubharmonic functions on unbounded domains