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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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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International