Published Paper
Inserted: 29 sep 2024
Last Updated: 22 may 2026
Journal: Journal of Differential Equations
Year: 2025
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.
Download: