Corpus ID: 16234535

# Volume and Area Renormalizations for Conformally Compact Einstein Metrics

@inproceedings{Graham1999VolumeAA,
title={Volume and Area Renormalizations for Conformally Compact Einstein Metrics},
author={C. Robin Graham},
year={1999}
}
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… Expand
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