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Volume and area renormalizations for conformally compact Einstein metrics

Graham, Robin C. — 2000

Proceedings of the 19th Winter School "Geometry and Physics"

Let X be the interior of a compact manifold X ¯ of dimension n + 1 with boundary M = ∂ X , and g + be a conformally compact metric on X , namely g ¯ ≡ r 2 g + 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 , d r ≠ 0 on M . The restrction of g ¯ to T M 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...

Jet isomorphism for conformal geometry

Robin C. Graham — 2007

Archivum Mathematicum

Jet isomorphism theorems for conformal geometry are discussed. A new proof of the jet isomorphism theorem for odd-dimensional conformal geometry is outlined, using an ambient realization of the conformal deformation complex. An infinite order ambient lift for conformal densities in the case in which harmonic extension is obstructed is described. A jet isomorphism theorem for even dimensional conformal geometry is formulated using the inhomogeneous ambient metrics recently introduced by the author...

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