Positive scalar curvature with skeleton singularities
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Author(s)
Li, Chao
Mantoulidis, Christos A
Date Issued
September 2018
Journal
Mathematische Annalen
Publisher
Springer Science and Business Media LLC
Citation
Li, Chao and Christos Mantoulidis. "Positive scalar curvature with skeleton singularities." Mathematische Annalen 374, 1-2 (September 2018): 99–131 © 2018 Springer-Verlag
Version
Author's final manuscript
Abstract
We study positive scalar curvature on the regular part of Riemannian manifolds with singular, uniformly Euclidean (
L∞) metrics that consolidate Gromov’s scalar curvature polyhedral comparison theory and edge metrics that appear in the study of Einstein manifolds. We show that, in all dimensions, edge singularities with cone angles ≤ 2 π along codimension-2 submanifolds do not affect the Yamabe type. In three dimensions, we prove the same for more general singular sets, which are allowed to stratify along 1-skeletons, exhibiting edge singularities (angles ≤ 2π) and arbitrary L∞ isolated point singularities. We derive, as an application of our techniques, Positive Mass Theorems for asymptotically flat manifolds with analogous singularities.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00208-018-1753-1
