具有有界里奇曲率的四流形上单形的波恩卡莱不等式

IF 0.5 4区 数学 Q3 MATHEMATICS
Shouhei Honda, Andrea Mondino
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引用次数: 0

摘要

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Poincaré inequality for one-forms on four manifolds with bounded Ricci curvature

In this short note, we provide a quantitative global Poincaré inequality for one-forms on a closed Riemannian four manifold, in terms of an upper bound on the diameter, a positive lower bound on the volume, and a two-sided bound on the Ricci curvature. This seems to be the first non-trivial result giving such an inequality without any higher curvature assumptions. The proof is based on a Hodge theoretic result on orbifolds, a comparison for fundamental groups, and a spectral convergence with respect to Gromov–Hausdorff convergence, via a degeneration result to orbifolds by Anderson.

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来源期刊
Archiv der Mathematik
Archiv der Mathematik 数学-数学
CiteScore
1.10
自引率
0.00%
发文量
117
审稿时长
4-8 weeks
期刊介绍: Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.
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