An Alternative Proof for the Upper Bound of Curvature Integral on Manifolds with Lower Sectional Curvature Bound
Year: 2025
Author: Nan Li
Journal of Mathematical Study, Vol. 58 (2025), Iss. 2 : pp. 164–174
Abstract
Petrunin proved that the integral of scalar curvature in a unit ball is bounded from above in terms of the dimension of the manifold and the lower bound of the sectional curvature. In this paper, we give an alternative proof for this result. The main difference between this proof and Petrunin’s original proof is that we construct a stratified finite covering and apply it directly to the given manifold, rather than arguing by contradiction for a sequence of manifolds, which satisfy some technical lifting properties.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v58n2.25.03
Journal of Mathematical Study, Vol. 58 (2025), Iss. 2 : pp. 164–174
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Scalar curvature sectional curvature $L^1$-norm Alexandrov space stratification covering.