Fully non-linear degenerate elliptic equations in complex geometry

Jianchun Chu*, Nicholas McCleerey

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We derive an a priori real Hessian estimate for solutions of a large family of geometric fully non-linear elliptic equations on compact Hermitian manifolds, which is independent of a lower bound for the right-hand side function. This improves on the estimates of Székelyhidi [57] and additionally applies to elliptic equations with a degenerate right-hand side. As an application, we establish the optimal C1,1 regularity of envelopes of (θ,m)-subharmonic functions on compact Hermitian manifolds.

Original languageEnglish (US)
Article number109176
JournalJournal of Functional Analysis
Volume281
Issue number9
DOIs
StatePublished - Nov 1 2021
Externally publishedYes

Keywords

  • Compact Hermitian manifolds
  • Fully non-linear degenerate elliptic equations

ASJC Scopus subject areas

  • Analysis

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