NNSC-Cobordism of Bartnik Data in High Dimensions
In this short note, we formulate three problems relating to nonnegative scalar curvature (NNSC) fill-ins. Loosely speaking, the first two problems focus on: When are (n−1)-dimensional Bartnik data (Σⁿ⁻¹ᵢ, γᵢ, Hᵢ), i=1,2, NNSC-cobordant? If (ⁿ⁻¹, γₛₜd, 0) is positive scalar curvature (PSC) cobordant...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2020 |
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| Sprache: | Englisch |
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Інститут математики НАН України
2020
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210580 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | NNSC-Cobordism of Bartnik Data in High Dimensions. Xue Hu and Yuguang Shi. SIGMA 16 (2020), 030, 5 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862532092680732672 |
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| author | Hu, Xue Shi, Yuguang |
| author_facet | Hu, Xue Shi, Yuguang |
| citation_txt | NNSC-Cobordism of Bartnik Data in High Dimensions. Xue Hu and Yuguang Shi. SIGMA 16 (2020), 030, 5 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this short note, we formulate three problems relating to nonnegative scalar curvature (NNSC) fill-ins. Loosely speaking, the first two problems focus on: When are (n−1)-dimensional Bartnik data (Σⁿ⁻¹ᵢ, γᵢ, Hᵢ), i=1,2, NNSC-cobordant? If (ⁿ⁻¹, γₛₜd, 0) is positive scalar curvature (PSC) cobordant to (Σⁿ⁻¹₁,γ₁, H₁), where (ⁿ⁻¹, γₛₜd) denotes the standard round unit sphere, then (Σⁿ⁻¹₁,γ₁, H₁) admits an NNSC fill-in. Just as Gromov's conjecture is connected with the positive mass theorem, our problems are connected with the Penrose inequality, at least in the case of n=3. Our third problem is on Λ(Σⁿ⁻¹, γ) defined below.
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| first_indexed | 2025-12-17T12:03:33Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-210580 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-17T12:03:33Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
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| spelling | Hu, Xue Shi, Yuguang 2025-12-12T10:16:59Z 2020 NNSC-Cobordism of Bartnik Data in High Dimensions. Xue Hu and Yuguang Shi. SIGMA 16 (2020), 030, 5 pages 1815-0659 2020 Mathematics Subject Classification: 53C20; 83C99 arXiv:2001.05607 https://nasplib.isofts.kiev.ua/handle/123456789/210580 https://doi.org/10.3842/SIGMA.2020.030 In this short note, we formulate three problems relating to nonnegative scalar curvature (NNSC) fill-ins. Loosely speaking, the first two problems focus on: When are (n−1)-dimensional Bartnik data (Σⁿ⁻¹ᵢ, γᵢ, Hᵢ), i=1,2, NNSC-cobordant? If (ⁿ⁻¹, γₛₜd, 0) is positive scalar curvature (PSC) cobordant to (Σⁿ⁻¹₁,γ₁, H₁), where (ⁿ⁻¹, γₛₜd) denotes the standard round unit sphere, then (Σⁿ⁻¹₁,γ₁, H₁) admits an NNSC fill-in. Just as Gromov's conjecture is connected with the positive mass theorem, our problems are connected with the Penrose inequality, at least in the case of n=3. Our third problem is on Λ(Σⁿ⁻¹, γ) defined below. The authors would like to thank Dr. Georg Frenck for his comments to clarify some notions in this note, and are also deeply grateful to anonymous referees for invaluable suggestions on the exposition. The research of the first and the second author was partially supported by NSFC 11701215, NSFC 11671015, and 11731001, respectively. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications NNSC-Cobordism of Bartnik Data in High Dimensions Article published earlier |
| spellingShingle | NNSC-Cobordism of Bartnik Data in High Dimensions Hu, Xue Shi, Yuguang |
| title | NNSC-Cobordism of Bartnik Data in High Dimensions |
| title_full | NNSC-Cobordism of Bartnik Data in High Dimensions |
| title_fullStr | NNSC-Cobordism of Bartnik Data in High Dimensions |
| title_full_unstemmed | NNSC-Cobordism of Bartnik Data in High Dimensions |
| title_short | NNSC-Cobordism of Bartnik Data in High Dimensions |
| title_sort | nnsc-cobordism of bartnik data in high dimensions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210580 |
| work_keys_str_mv | AT huxue nnsccobordismofbartnikdatainhighdimensions AT shiyuguang nnsccobordismofbartnikdatainhighdimensions |