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Weakly asymptotically hyperbolic solutions to the Einstein constraint equations Allen, Paul T
Description
We introduce a class of ``weakly asymptotically hyperbolic'' geometries whose sectional curvatures tend to \(-1\) and are \(C^0\) but not necessarily \(C^2\) conformally compact. We establish Fredholm results for geometric elliptic operators in this setting.
We use these results to construct constant-mean-curvature solutions to the Einstein constraint equations in the weakly asymptotically hyperbolic setting. We furthermore can ensure that our solutions satisfy the shear-free condition, which is necessary for any spacetime development to admit a regular conformal boundary at future null infinity.
This is joint work with James Isenberg, John M. Lee, and Iva Stavrov Allen.
Item Metadata
| Title |
Weakly asymptotically hyperbolic solutions to the Einstein constraint equations
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| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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| Date Issued |
2016-07-20T09:30
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| Description |
We introduce a class of ``weakly asymptotically hyperbolic'' geometries whose sectional curvatures tend to \(-1\) and are \(C^0\) but not necessarily \(C^2\) conformally compact. We establish Fredholm results for geometric elliptic operators in this setting.
We use these results to construct constant-mean-curvature solutions to the Einstein constraint equations in the weakly asymptotically hyperbolic setting. We furthermore can ensure that our solutions satisfy the shear-free condition, which is necessary for any spacetime development to admit a regular conformal boundary at future null infinity.
This is joint work with James Isenberg, John M. Lee, and Iva Stavrov Allen.
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| Extent |
22 minutes
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| Subject | |
| Type | |
| File Format |
video/mp4
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| Language |
eng
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| Notes |
Author affiliation: Lewis & Clark College
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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 |
10.14288/1.0340782
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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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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International