January, 2023 Comparison geometry of manifolds with boundary under lower $N$-weighted Ricci curvature bounds with $\varepsilon$-range
Kazuhiro KUWAE, Yohei SAKURAI
Author Affiliations +
J. Math. Soc. Japan 75(1): 151-172 (January, 2023). DOI: 10.2969/jmsj/87278727

Abstract

We study comparison geometry of manifolds with boundary under a lower $N$-weighted Ricci curvature bound for $N \in ] -\infty, 1] \cup [n, +\infty]$ with $\varepsilon$-range introduced by Lu–Minguzzi–Ohta in 2022. We will conclude splitting theorems, and also comparison geometric results for inscribed radius, volume around the boundary, and smallest Dirichlet eigenvalue of the weighted $p$-Laplacian. Our results interpolate those for $N \in [n, +\infty[$ and $\varepsilon = 1$, and for $N \in ] -\infty, 1]$ and $\varepsilon = 0$ by the second named author.

Funding Statement

The first named author was supported in part by JSPS Grant-in-Aid for Scientific Research (KAKENHI) 17H02846 and by fund (No.185001) from the Central Research Institute of Fukuoka University. The second named author was supported in part by JSPS Grant-in-Aid for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials Design” 17H06460.

Citation

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Kazuhiro KUWAE. Yohei SAKURAI. "Comparison geometry of manifolds with boundary under lower $N$-weighted Ricci curvature bounds with $\varepsilon$-range." J. Math. Soc. Japan 75 (1) 151 - 172, January, 2023. https://doi.org/10.2969/jmsj/87278727

Information

Received: 5 July 2021; Published: January, 2023
First available in Project Euclid: 8 July 2022

MathSciNet: MR4539013
zbMATH: 1520.53027
Digital Object Identifier: 10.2969/jmsj/87278727

Subjects:
Primary: 53C21
Secondary: 53C20

Keywords: $N$-weighted Ricci curvature , Dirichlet eigenvalue , inscribed radius , Laplacian comparison theorem , splitting theorem , volume comparison theorem , weighted $p$-Laplacian , weighted mean curvature

Rights: Copyright ©2023 Mathematical Society of Japan

Vol.75 • No. 1 • January, 2023
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