- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- BIRS Workshop Lecture Videos /
- Asymptotically hyperbolic extensions and estimates...
Open Collections
BIRS Workshop Lecture Videos
BIRS Workshop Lecture Videos
Asymptotically hyperbolic extensions and estimates for an analogue of the Bartnik mass McCormick, Stephen
Description
Given a metric $g$ on the $2$-sphere $S^2$ with Gaussian curvature bound below by $-3$, and non-negative constant $H$, we construct asymptotically hyperbolic manifolds whose boundary is isometric to $(S^2, g)$ and has mean curvature $H$ (with respect to the inward-pointing unit normal). These AH manifolds have mass that is controlled in terms of $g$ and $H$, reducing to the hyperbolic Hawking mass of $(S^2, g, H)$ as $g$ becomes round or $H$ tends to zero. This gives an upper bound for an asymptotically hyperbolic analogue of the Bartnik mass. The construction is based on work of Mantoulidis and Schoen, where they used similar ideas to effectively compute the (usual AF) Bartnik mass of apparent horizons. This is joint work with Armando Cabrera Pacheco and Carla Cederbaum.
Item Metadata
Title |
Asymptotically hyperbolic extensions and estimates for an analogue of the Bartnik mass
|
Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
|
Date Issued |
2018-05-16T10:15
|
Description |
Given a metric $g$ on the $2$-sphere $S^2$ with Gaussian curvature bound below by $-3$, and non-negative constant $H$, we construct asymptotically hyperbolic manifolds whose boundary is isometric to $(S^2, g)$ and has mean curvature $H$ (with respect to the inward-pointing unit normal). These AH manifolds have mass that is controlled in terms of $g$ and $H$, reducing to the hyperbolic Hawking mass of $(S^2, g, H)$ as $g$ becomes round or $H$ tends to zero. This gives an upper bound for an asymptotically hyperbolic analogue of the Bartnik mass. The construction is based on work of Mantoulidis and Schoen, where they used similar ideas to effectively compute the (usual AF) Bartnik mass of apparent horizons. This is joint work with Armando Cabrera Pacheco and Carla Cederbaum.
|
Extent |
30.0
|
Subject | |
Type | |
File Format |
video/mp4
|
Language |
eng
|
Notes |
Author affiliation: Uppsala Universitet
|
Series | |
Date Available |
2019-03-21
|
Provider |
Vancouver : University of British Columbia Library
|
Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
DOI |
10.14288/1.0377278
|
URI | |
Affiliation | |
Peer Review Status |
Unreviewed
|
Scholarly Level |
Postdoctoral
|
Rights URI | |
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International