Preprint

Inserted: 29 sep 2024
Last Updated: 29 sep 2024

Year: 2024

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.