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
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
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