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Research Papers
A lower bound for the curvature integral under an upper curvature bound
T. Fujioka Department of Mathematics, Osaka University, Toyonaka, Osaka 560-0043, Japan
Abstract:
It is proved that the integral of the scalar curvature over a Riemannian manifold is uniformly bounded below in terms of its dimension, upper bounds on the sectional curvature and volume, and a lower bound on the injectivity radius. This is an analog of an earlier result of Petrunin for Riemannian manifolds with sectional curvature bounded below.
Keywords:
sectional curvature, scalar curvature, Gromov–Hausdorff convergence, GCBA spaces, strainers.
Received: 23.12.2023
Citation:
T. Fujioka, “A lower bound for the curvature integral under an upper curvature bound”, Algebra i Analiz, 36:2 (2024), 131–160
Linking options:
https://www.mathnet.ru/eng/aa1913 https://www.mathnet.ru/eng/aa/v36/i2/p131
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Statistics & downloads: |
Abstract page: | 198 | Full-text PDF : | 1 | References: | 30 | First page: | 24 |
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