Rigidity phenomena on lower N-weighted Ricci curvature bounds with ε-range for non-symmetric Laplacian

2020/09/25 by Kazuhiro Kuwae, Kuwae, Kazuhiro, Yohei Sakurai +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2009.12012

openalex publication_date 2020/09/25 · openalex created_date 2020/10/01 · openalex updated_date 2026/07/28

Abstract

Lu-Minguzzi-Ohta have introduced the notion of a lower N-weighted Ricci curvature bound with ε-range, and derived several comparison geometric estimates from a Laplacian comparison theorem for weighted Laplacian. The aim of this paper is to investigate various rigidity phenomena for the equality case of their comparison geometric results. We will obtain rigidity results concerning the Laplacian comparison theorem, diameter comparisons, and volume comparisons. We also generalize their works for non-symmetric Laplacian induced from vector field potential.

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