Dihedral Rigidity of Parabolic Polyhedrons in Hyperbolic Spaces
In this note, we establish the dihedral rigidity phenomenon for a collection of parabolic polyhedra enclosed by horospheres in hyperbolic manifolds, extending Gromov's comparison theory to metrics with negative scalar curvature lower bounds. Our result is a localization of the positive mass the...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211021 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Dihedral Rigidity of Parabolic Polyhedrons in Hyperbolic Spaces. Chao Li. SIGMA 16 (2020), 099, 8 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862639224452284416 |
|---|---|
| author | Li, Chao |
| author_facet | Li, Chao |
| citation_txt | Dihedral Rigidity of Parabolic Polyhedrons in Hyperbolic Spaces. Chao Li. SIGMA 16 (2020), 099, 8 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this note, we establish the dihedral rigidity phenomenon for a collection of parabolic polyhedra enclosed by horospheres in hyperbolic manifolds, extending Gromov's comparison theory to metrics with negative scalar curvature lower bounds. Our result is a localization of the positive mass theorem for asymptotically hyperbolic manifolds. We also motivate and formulate some open questions concerning related rigidity phenomena and convergence of metrics with scalar curvature lower bounds.
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| first_indexed | 2026-03-15T03:35:21Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211021 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T03:35:21Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Li, Chao 2025-12-22T09:31:10Z 2020 Dihedral Rigidity of Parabolic Polyhedrons in Hyperbolic Spaces. Chao Li. SIGMA 16 (2020), 099, 8 pages 1815-0659 2020 Mathematics Subject Classification: 53C21; 53A10 arXiv:2007.12563 https://nasplib.isofts.kiev.ua/handle/123456789/211021 https://doi.org/10.3842/SIGMA.2020.099 In this note, we establish the dihedral rigidity phenomenon for a collection of parabolic polyhedra enclosed by horospheres in hyperbolic manifolds, extending Gromov's comparison theory to metrics with negative scalar curvature lower bounds. Our result is a localization of the positive mass theorem for asymptotically hyperbolic manifolds. We also motivate and formulate some open questions concerning related rigidity phenomena and convergence of metrics with scalar curvature lower bounds. I would like to thank Christina Sormani and Misha Gromov for organizing the excellent workshop Emerging Topics on Scalar Curvature and Convergence at the Institute for Advanced Study, and everyone in the workshop for valuable discussions. The author is supported by NSF grant DMS-2005287. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Dihedral Rigidity of Parabolic Polyhedrons in Hyperbolic Spaces Article published earlier |
| spellingShingle | Dihedral Rigidity of Parabolic Polyhedrons in Hyperbolic Spaces Li, Chao |
| title | Dihedral Rigidity of Parabolic Polyhedrons in Hyperbolic Spaces |
| title_full | Dihedral Rigidity of Parabolic Polyhedrons in Hyperbolic Spaces |
| title_fullStr | Dihedral Rigidity of Parabolic Polyhedrons in Hyperbolic Spaces |
| title_full_unstemmed | Dihedral Rigidity of Parabolic Polyhedrons in Hyperbolic Spaces |
| title_short | Dihedral Rigidity of Parabolic Polyhedrons in Hyperbolic Spaces |
| title_sort | dihedral rigidity of parabolic polyhedrons in hyperbolic spaces |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211021 |
| work_keys_str_mv | AT lichao dihedralrigidityofparabolicpolyhedronsinhyperbolicspaces |