Published March 9, 2021
| public
Discussion Paper
Bounded sectional curvature and essential minimal volume
- Creators
- Song, Antoine
Chicago
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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.
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.Additional details
- Eprint ID
- 117592
- Resolver ID
- CaltechAUTHORS:20221026-539117000.3
- Clay Mathematics Institute
- Created
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2022-10-28Created from EPrint's datestamp field
- Updated
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2022-10-28Created from EPrint's last_modified field