Volume and area renormalizations for conformally compact Einstein metrics

Graham, Robin C.. "Volume and area renormalizations for conformally compact Einstein metrics." Proceedings of the 19th Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 2000. 31-42. <http://eudml.org/doc/221675>.

@inProceedings{Graham2000,
abstract = {Let $X$ be the interior of a compact manifold $\overline\{X\}$ of dimension $n+1$ with boundary $M=\partial X$, and $g_+$ be a conformally compact metric on $X$, namely $\overline\{g\}\equiv r^2g_+$ extends continuously (or with some degree of smoothness) as a metric to $X$, where $r$ denotes a defining function for $M$, i.e. $r>0$ on $X$ and $r=0$, $dr\ne 0$ on $M$. The restrction of $\overline\{g\}$ to $TM$ rescales upon changing $r$, so defines invariantly a conformal class of metrics on $M$, which is called the conformal infinity of $g_+$. In the present paper, the author considers conformally compact metrics satisfying the Einstein condition Ric$(g_+)=-ng_+$, which are called conformally compact Einstein metrics on $X$, and their extensions to $X$ together with the restrictions of $\overline\{g\}$ to the boundary $M=\partial X$. First, the author notes that a representative metric $g$ on $M$ for the conformal infinity of a conformally compact Einstein metric},
author = {Graham, Robin C.},
booktitle = {Proceedings of the 19th Winter School "Geometry and Physics"},
keywords = {Proceedings; Winter school; Geometry; Physics; Srní (Czech Republic)},
location = {Palermo},
pages = {31-42},
publisher = {Circolo Matematico di Palermo},
title = {Volume and area renormalizations for conformally compact Einstein metrics},
url = {http://eudml.org/doc/221675},
year = {2000},
}

TY - CLSWK
AU - Graham, Robin C.
TI - Volume and area renormalizations for conformally compact Einstein metrics
T2 - Proceedings of the 19th Winter School "Geometry and Physics"
PY - 2000
CY - Palermo
PB - Circolo Matematico di Palermo
SP - 31
EP - 42
AB - Let $X$ be the interior of a compact manifold $\overline{X}$ of dimension $n+1$ with boundary $M=\partial X$, and $g_+$ be a conformally compact metric on $X$, namely $\overline{g}\equiv r^2g_+$ extends continuously (or with some degree of smoothness) as a metric to $X$, where $r$ denotes a defining function for $M$, i.e. $r>0$ on $X$ and $r=0$, $dr\ne 0$ on $M$. The restrction of $\overline{g}$ to $TM$ rescales upon changing $r$, so defines invariantly a conformal class of metrics on $M$, which is called the conformal infinity of $g_+$. In the present paper, the author considers conformally compact metrics satisfying the Einstein condition Ric$(g_+)=-ng_+$, which are called conformally compact Einstein metrics on $X$, and their extensions to $X$ together with the restrictions of $\overline{g}$ to the boundary $M=\partial X$. First, the author notes that a representative metric $g$ on $M$ for the conformal infinity of a conformally compact Einstein metric
KW - Proceedings; Winter school; Geometry; Physics; Srní (Czech Republic)
UR - http://eudml.org/doc/221675
ER -