2023/06/21 by Xinyue Cheng, Cheng, Xinyue, Yalu Feng +1
Physics and Astronomy · #53B40 #53C60 #58C35 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2306.12260
openalex publication_date 2023/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study functional and geometric inequalities on complete Finsler measure spaces under the condition that the weighted Ricci curvature \rm Ric_∞ has a lower bound. We first obtain some local uniform Poincaré inequalities and Sobolev inequalities. Further, we give a mean value inequality for nonnegative subsolutions of elliptic equations. Finally, we obtain local and global Harnack inequalities, and then, establish a global gradient estimate for positive harmonic functions on forward complete non-compact Finsler measure spaces. Besides, as a by-product of the mean value inequality, we prove a Liouville type theorem.