Linearized heat semigroups on Finsler measure spaces and some applications

2023/07/01 by Qiaoling Xia, Xia, Qiaoling
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2307.00272

openalex publication_date 2023/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is known that the Finsler heat flow is a nonlinear flow. This leads to the study of linearized heat semigroups for the Finsler heat flow. In this paper, we give the properties of linearized heat semigroups and prove that the semigroup is conservative on complete Finsler measure spaces (M, F, m) with weighted Ricci curvature Ric_N bounded from below. As applications, we give new proofs of Li-Yau's inequalities established in \citeXia2 and \citeOS2 respectively in the compact case and extend them to the complete Finsler measure spaces with Ric_N≥ K for K∈ \mathbb R. Finally we give several equivalent characterizations of Ric_∞≥ K (K∈ \mathbb R) via the linearized heat semigroup approach and their applications.

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