Year: 2024
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Liu, Junbang
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403963862