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Total mean curvature, scalar curvature, and a variational analog of Brown-York mass Miao, Pengzi
Description
We discuss the supremum of the total boundary mean curvature of compact, mean- convex 3-manifolds with nonnegative scalar curvature, with prescribed intrinsic boundary metric. We establish an additivity property for the supremum and exhibit rigidity for maximizers as- suming the supremum is attained. When the boundary consists of topological 2-spheres, we demonstrate that the finiteness of the supremum follows from the previous work of Shi-Tam and
Wang-Yau on the quasi-local mass problem in general relativity. In turn, we define a varia- tional analog of the Brown-York mass without assuming the boundary surface has positive Gauss curvature. This is a joint work with Christos Mantoulidis.
Item Metadata
| Title |
Total mean curvature, scalar curvature, and a variational analog of Brown-York mass
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| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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| Date Issued |
2016-07-19T10:31
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| Description |
We discuss the supremum of the total boundary mean curvature of compact, mean- convex 3-manifolds with nonnegative scalar curvature, with prescribed intrinsic boundary metric. We establish an additivity property for the supremum and exhibit rigidity for maximizers as- suming the supremum is attained. When the boundary consists of topological 2-spheres, we demonstrate that the finiteness of the supremum follows from the previous work of Shi-Tam and
Wang-Yau on the quasi-local mass problem in general relativity. In turn, we define a varia- tional analog of the Brown-York mass without assuming the boundary surface has positive Gauss curvature. This is a joint work with Christos Mantoulidis.
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| Extent |
24 minutes
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| Subject | |
| Type | |
| File Format |
video/mp4
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| Language |
eng
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| Notes |
Author affiliation: University of Miami
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| Series | |
| Date Available |
2017-02-04
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0340757
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| URI | |
| Affiliation | |
| Peer Review Status |
Unreviewed
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| Scholarly Level |
Faculty
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| Rights URI | |
| Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International