Non UBC
DSpace
Singer, Michael
2019-03-21T05:02:59Z
2018-05-14T10:29
Let $M$ be a compact oriented $d$-dimensional manifold with boundary $N$. A natural geometric boundary value problem is to find an asymptotically hyperbolic Einstein metric $g$ on (the interior of) $M$ with prescribed `conformal infinityĆ¢ on $N$. A little more precisely, the problem is to find (Einstein) $g$ with the boundary condition $x^2g$ tends to a metric $h$ on $N$ as $x$ goes to $0$, $x$ being a boundary defining function for $N$. The freedom to rescale $x$ by an arbitrary smooth positive function means that only the conformal class of $h$ is naturally well defined. Hence the terminology `conformal infinityĆ¢ in this boundary problem. Since the pioneering work of Graham and Lee (1991) the problem has attracted attention from a number of authors.
If the dimension $d$ is $4$, there is a refinement, asking that $g$ be anti-self-dual as well as Einstein (satisfying the same boundary condition). If $M$ is the ball, this is the subject of the positive frequency conjecture of LeBrun (1980s) proved by Biquard in 2002.
In this talk, which is based on joint work with Joel Fine and Rafe Mazzeo, I shall explain a gauge theoretic approach to the ASDE problem which is readily applicable for general $M$ and the currently available results.
https://circle.library.ubc.ca/rest/handle/2429/69030?expand=metadata
60.0
video/mp4
Author affiliation: University College London
Banff (Alta.)
10.14288/1.0377270
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Faculty
BIRS Workshop Lecture Videos (Banff, Alta)
Mathematics
Global analysis, analysis on manifolds
Relativity and gravitational theory
Global analysis
On asymptotically hyperbolic anti-self-dual Einstein metrics
Moving Image
http://hdl.handle.net/2429/69030