The parabolic Monge-Ampère equation on compact almost Hermitian manifolds

Jianchun Chu

doi:10.1515/crelle-2018-0019

The parabolic Monge-Ampère equation on compact almost Hermitian manifolds

Jianchun Chu^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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 language	English (US)
Pages (from-to)	1-24
Number of pages	24
Journal	Journal fur die Reine und Angewandte Mathematik
Volume	2020
Issue number	761
DOIs	https://doi.org/10.1515/crelle-2018-0019
State	Published - Apr 1 2020

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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abstract = "We prove the long time existence and uniqueness of solutions to the parabolic Monge-Amp{\`e}re 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-Amp{\`e}re equation. This gives a parabolic proof of existence of solutions to the Monge-Amp{\`e}re equation on almost Hermitian manifolds.",

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AB - 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.

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The parabolic Monge-Ampère equation on compact almost Hermitian manifolds

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