# Einstein metrics with prescribed conformal infinity on the ball

@article{Graham1991EinsteinMW,
title={Einstein metrics with prescribed conformal infinity on the ball},
author={C. Robin Graham and John M. Lee},
year={1991},
volume={87},
pages={186-225}
}
• Published 1 June 1991
• Mathematics
In this paper we study a boundary problem for Einstein metrics. Let A4 be the interior of a compact (n + l)-dimensional manifold-with-boundary I@, and g a Riemannian metric on M. If 2 is a metric on bM, we say the conformal class [S] is the conformal infinity of g if, for some defining function p E P(ii;i) that is positive in A4 and vanishes to first order on bM, p2g extends continuously to A and p’g 1 TbM is conformal to g. It is clear that this an invariant notion, independent of the choice… Expand
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