2007/12/19 by Feng-Yu Wang, Feng‐Yu Wang, Wang, Feng-Yu
Mathematics · #58G32 #60J60 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Point processes and geometric inequalities #Probability (math.PR) #math.DG #math.PR #msc:58G32 #msc:60J60
paper · pdf · doi:10.48550/arxiv.0712.3142
arxiv created 2007/12/19 · openalex publication_date 2007/12/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive weighted log-Sobolev inequalities from a class of super Poincaré inequalities. As an application, the Talagrand inequality with larger distances are obtained. In particular, on a complete connected Riemannian manifold, we prove that the log^\dd-Sobolev inequality with \dd∈ (1,2) implies the L2/(2-\dd)-transportation cost inequality W^\rr2/(2-\dd)(fμ,μ)2/(2-\dd)≤ Cμ(flog f), μ(f)=1, f≥ 0 for some constant C>0, and they are equivalent if the curvature of the corresponding generator is bounded below. Weighted log-Sobolev and entropy-cost inequalities are also derived for a large class of probability measures on \Rd.