The parabolic Monge-Ampère equation on compact almost Hermitian manifolds

Jianchun Chu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We prove the long time existence and uniqueness of solutions to the parabolic Monge-Ampère equation on compact almost Hermitian manifolds. We also show that the normalization of solution converges to a smooth function in C ∞ topology as t → ∞. Up to scaling, the limit function is a solution of the Monge-Ampère equation. This gives a parabolic proof of existence of solutions to the Monge-Ampère equation on almost Hermitian manifolds.

Original languageEnglish (US)
Pages (from-to)1-24
Number of pages24
JournalJournal fur die Reine und Angewandte Mathematik
Volume2020
Issue number761
DOIs
StatePublished - Apr 1 2020

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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