Positive scalar curvature with skeleton singularities
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,...
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| Format: | Article |
| Language: | English |
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Springer Science and Business Media LLC
2020
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| Online Access: | https://hdl.handle.net/1721.1/128429 |
| _version_ | 1826198833311252480 |
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| author | Li, Chao Mantoulidis, Christos A |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Li, Chao Mantoulidis, Christos A |
| author_sort | Li, Chao |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T11:10:41Z |
| format | Article |
| id | mit-1721.1/128429 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:10:41Z |
| publishDate | 2020 |
| publisher | Springer Science and Business Media LLC |
| record_format | dspace |
| spelling | mit-1721.1/1284292022-10-01T01:51:19Z Positive scalar curvature with skeleton singularities Li, Chao Mantoulidis, Christos A Massachusetts Institute of Technology. Department of Mathematics 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. 2020-11-09T16:56:40Z 2020-11-09T16:56:40Z 2018-09 2018-01 2020-09-24T20:46:46Z Article http://purl.org/eprint/type/JournalArticle 0025-5831 1432-1807 https://hdl.handle.net/1721.1/128429 Li, Chao and Christos Mantoulidis. "Positive scalar curvature with skeleton singularities." Mathematische Annalen 374, 1-2 (September 2018): 99–131 © 2018 Springer-Verlag en https://doi.org/10.1007/s00208-018-1753-1 Mathematische Annalen 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. Springer-Verlag GmbH Germany, part of Springer Nature application/pdf Springer Science and Business Media LLC Springer Berlin Heidelberg |
| spellingShingle | Li, Chao Mantoulidis, Christos A Positive scalar curvature with skeleton singularities |
| title | Positive scalar curvature with skeleton singularities |
| title_full | Positive scalar curvature with skeleton singularities |
| title_fullStr | Positive scalar curvature with skeleton singularities |
| title_full_unstemmed | Positive scalar curvature with skeleton singularities |
| title_short | Positive scalar curvature with skeleton singularities |
| title_sort | positive scalar curvature with skeleton singularities |
| url | https://hdl.handle.net/1721.1/128429 |
| work_keys_str_mv | AT lichao positivescalarcurvaturewithskeletonsingularities AT mantoulidischristosa positivescalarcurvaturewithskeletonsingularities |