An upper bound of the heat kernel along the harmonic-Ricci flow

2015/01/04 by Shouwen Fang, Tao Zheng, Fang, Shouwen +1 · 1 citation
Mathematics · #53C21 #53C44 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #math.DG #msc:53C21 #msc:53C44

paper · pdf · doi:10.48550/arxiv.1501.00639

16pages. arXiv admin note: text overlap with arXiv:1412.3200 by other authors

openalex publication_date 2015/01/04 · arxiv created 2015/02/27 · arxiv updated 2015/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we first derive a Sobolev inequality along the harmonic-Ricci flow. We then prove a linear parabolic estimate based on the Sobolev inequality and Moser's iteration. As an application, we will obtain an upper bound estimate for the heat kernel under the flow.

Citations

• On the parabolic kernel of the Schrödinger operator

Cited by

• Long time existence and bounded scalar curvature in the Ricci-harmonic flow

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