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December 2021 Rigidity phenomena on lower N-weighted Ricci curvature bounds with ε-range for nonsymmetric Laplacian
Kazuhiro Kuwae, Yohei Sakurai
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Illinois J. Math. 65(4): 847-868 (December 2021). DOI: 10.1215/00192082-9619586

Abstract

Lu, Minguzzi, and Ohta 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 a 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 a nonsymmetric Laplacian induced from vector field potential.

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Kazuhiro Kuwae. Yohei Sakurai. "Rigidity phenomena on lower N-weighted Ricci curvature bounds with ε-range for nonsymmetric Laplacian." Illinois J. Math. 65 (4) 847 - 868, December 2021. https://doi.org/10.1215/00192082-9619586

Information

Received: 17 February 2021; Revised: 25 October 2021; Published: December 2021
First available in Project Euclid: 2 December 2021

Digital Object Identifier: 10.1215/00192082-9619586

Subjects:
Primary: 53C21
Secondary: 53C20

Rights: Copyright © 2021 by the University of Illinois at Urbana–Champaign

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Vol.65 • No. 4 • December 2021
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