C1,1 regularity for degenerate complex Monge–Ampère equations and geodesic rays

Jianchun Chu, Valentino Tosatti*, Benjamin Weinkove

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We prove a C1,1 estimate for solutions of complex Monge–Ampère equations on compact Kähler manifolds with possibly nonempty boundary, in a degenerate cohomology class. This strengthens previous estimates of Phong–Sturm. As applications we deduce the local C1,1 regularity of geodesic rays in the space of Kähler metrics associated to a test configuration, as well as the local C1,1 regularity of quasi-psh envelopes in nef and big classes away from the non-Kähler locus.

Original languageEnglish (US)
Pages (from-to)292-312
Number of pages21
JournalCommunications in Partial Differential Equations
Volume43
Issue number2
DOIs
StatePublished - Feb 1 2018

Keywords

  • C regularity
  • complex Monge–Ampere equations
  • geodesic rays
  • quasi-psh envelopes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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