Volume growth and on-diagonal heat kernel bounds on Riemannian manifolds with an end

2022/01/14 by Alexander Grigorʼyan, Alexander Grigor'yan, Grigor'yan, Alexander +2
Computer Science · Mathematics · #31B05 #58J35 #60J65 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Combinatorics #Diagonal #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry #Heat kernel #Kernel (algebra) #Mathematical analysis #Mathematics #Nonlinear Partial Differential Equations #Physics #Probability (math.PR) #Pure mathematics #Thermodynamics #Volume (thermodynamics) #math.AP #math.DG #math.PR #msc:31B05 #msc:58J35 #msc:60J65

paper · pdf · doi:10.48550/arxiv.2201.05695

30 pages

arxiv created 2022/01/14 · openalex publication_date 2022/01/14 · arxiv updated 2022/01/19 · openalex created_date 2022/04/03 · openalex updated_date 2026/08/06

Abstract

We investigate heat kernel estimates of the form p_t(x, x)≥ c_xt^-α, for large enough t, where α and c_x are positive reals and c_x may depend on x, on manifolds having at least one end.

Related

• Heat kernel Gaussian bounds on manifolds I: manifolds with non-negative Ricci curvature
• Heat kernel estimates on connected sums of parabolic manifolds
• Heat kernel estimates on manifolds with ends with mixed boundary condition
• Large time behavior of the on-diagonal heat kernel for minimal submanifolds with polynomial volume growth
• Geometric analysis on manifolds with ends