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 (𝕊ⁿ⁻¹, γₛₜd, 0) is positive scalar curvature (PSC) cobordant...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210580 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| Summary: | 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 (𝕊ⁿ⁻¹, γₛₜd, 0) is positive scalar curvature (PSC) cobordant to (Σⁿ⁻¹₁,γ₁, H₁), where (𝕊ⁿ⁻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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| ISSN: | 1815-0659 |