ABP estimate on metric measure spaces via optimal transport
Metric Geometry
2024-08-21 v1 Analysis of PDEs
Differential Geometry
Functional Analysis
Abstract
By using optimal transport theory, we establish a sharp Alexandroff--Bakelman--Pucci (ABP) type estimate on metric measure spaces with synthetic Riemannian Ricci curvature lower bounds, and prove some geometric and functional inequalities including a functional ABP estimate. Our result not only extends the border of ABP estimate, but also provides an effective substitution of Jacobi fields computation in the non-smooth framework, which has potential applications to many problems in non-smooth geometric analysis.
Keywords
Cite
@article{arxiv.2408.10725,
title = {ABP estimate on metric measure spaces via optimal transport},
author = {Bang-Xian Han},
journal= {arXiv preprint arXiv:2408.10725},
year = {2024}
}