On relative $L^\infty$ estimate for complex Monge-Ampère equations

Fuente: arXiv
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Main Author: Liu, Junbang
Format: Preprint
Published: 2024
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author Liu, Junbang
author_facet Liu, Junbang
contents We prove a relative $L^\infty$ estimate for a class of complex Monge-Ampère type equations on Kähler manifolds. It provides a unified approach to Tundinger type estimate and uniform estimate. It also improves the previous results about modulus of continuity, stability estimates, and $W^{1,1}$-estimates of Green's functions. The argument is based on the PDE method developed by Guo-Phong-Tong and constructing appropriate comparison metrics from entropy bound.
format Preprint
id arxiv_https___arxiv_org_abs_2410_04393
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On relative $L^\infty$ estimate for complex Monge-Ampère equations
Liu, Junbang
Differential Geometry
Analysis of PDEs
We prove a relative $L^\infty$ estimate for a class of complex Monge-Ampère type equations on Kähler manifolds. It provides a unified approach to Tundinger type estimate and uniform estimate. It also improves the previous results about modulus of continuity, stability estimates, and $W^{1,1}$-estimates of Green's functions. The argument is based on the PDE method developed by Guo-Phong-Tong and constructing appropriate comparison metrics from entropy bound.
title On relative $L^\infty$ estimate for complex Monge-Ampère equations
topic Differential Geometry
Analysis of PDEs
url https://arxiv.org/abs/2410.04393