Calculus of Variations and Geometric Measure Theory

B. Han

ABP estimate on metric measure spaces via optimal transport

created by han1 on 29 Sep 2024
modified on 22 May 2026

[BibTeX]

Published Paper

Inserted: 29 sep 2024
Last Updated: 22 may 2026

Journal: Journal of Differential Equations
Year: 2025

ArXiv: 2408.10725 PDF

Abstract:

By using optimal transport theory, we establish a sharp Alexandroff– Bakelman–Pucci (ABP) type estimate on metric measure spaces with syn- thetic 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 effec- tive substitution of Jacobi fields computation in the non-smooth framework, which has potential applications to many problems in non-smooth geometric analysis.


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