2015/02/06 by Yong Lin, Shuang Liu, Lin, Yong +3
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #math.DG #math.FA
paper · pdf · doi:10.48550/arxiv.1502.01958
13 pages
arxiv created 2015/02/06 · openalex publication_date 2015/02/06 · arxiv updated 2015/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove the equivalent of ultracontractive bound of heat semigroup or the uniform upper bound of the heat kernel with the Nash inequality, Log-Sobolev inequalities on graphs. We also show that under the assumption of volume growth and nonnegative curvature CDE'(n,0) the Sobolev inequality, Nash inequality, Faber-Krahn inequality, Log-Sobolev inequalities, discrete and continuous-time uniform upper estimate of heat kernel are all true on graph.