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Bounded sectional curvature and essential minimal volume

Song, Antoine (2021) Bounded sectional curvature and essential minimal volume. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20221026-539117000.3

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Abstract

For a closed smooth manifold M, we consider a closure of the set of metrics on M with sectional curvature bounded between −1 and 1. We introduce a variant of Gromov's minimal volume, called essential minimal volume, defined as the infimum of the volume over this closure. We study metrics achieving the essential minimal volume, and prove estimates for negatively curved manifolds, Einstein 4-manifolds and complex surfaces with nonnegative Kodaira dimension.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://doi.org/10.48550/arXiv.2103.05659DOIDiscussion Paper
Additional Information:I am grateful to John Lott for numerous discussions that improved the results. I would also like to thank Song Sun, Aaron Naber, Xiaochun Rong, Ruobing Zhang, Ben Lowe for helpful conversations, and Claude LeBrun, Zoltán Szabó for comments. This research was conducted during the period the author served as a Clay Research Fellow.
Funders:
Funding AgencyGrant Number
Clay Mathematics InstituteUNSPECIFIED
DOI:10.48550/arXiv.2103.05659
Record Number:CaltechAUTHORS:20221026-539117000.3
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20221026-539117000.3
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:117592
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:28 Oct 2022 15:31
Last Modified:28 Oct 2022 15:31

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