Heat kernel upper bounds under the generalized curvature(-dimension) inequality

2013/08/28 by Huai Qian Li, LI, Huai Qian, Huai Qian LI
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1308.6131

arxiv created 2013/08/28 · openalex publication_date 2013/08/28 · arxiv updated 2013/08/29 · openalex created_date 2022/08/28 · openalex updated_date 2026/07/28

Abstract

In the sub-Riemannian manifolds, on the one hand, following Baudoin-Garofalo \citeBaudoinGarofalo, the upper bound for heat kernels associated to a class of locally subelliptic operators are given under the generalized curvature-dimension inequality with a negative curvature parameter; on the other hand, the argument combining Grigor'yan's integrated maximum principle with Wang's dimension-free Harnack inequality is also shown to derive the upper bound for the heat kernel under the generalized curvature inequality.

Citations

• Ricci curvature for metric-measure spaces via optimal transport
• On the parabolic kernel of the Schrödinger operator
• Quasi-invariance for heat kernel measures on sub-Riemannian infinite-dimensional Heisenberg groups

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