Hypoelliptic heat kernel inequalities on H-type groups

2014/06/07 by Nathaniel Eldredge, Eldredge, Nathaniel
Mathematics · #35H10 #53C17 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1406.1840

openalex publication_date 2014/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We study inequalities related to the heat kernel for the hypoelliptic sublaplacian on an H-type Lie group. Specifically, we obtain precise pointwise upper and lower bounds on the heat kernel function itself. We then apply these bounds to derive an estimate on the gradient of solutions of the heat equation, which is known to have various significant consequences including logarithmic Sobolev inequalities. We also present a computation of the heat kernel, and a discussion of the geometry of H-type groups including their geodesics and Carnot-Carathéodory distance functions.

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