Families of Conformally Covariant Differential Operators, Q-Curvature and Holography (Hardcover, 2009 ed.)

A basic problem in geometry is to ?nd canonical metrics on smooth manifolds. Such metrics can be speci?ed, for instance, by curvature conditions or extremality properties, and are expected to contain basic information on the topology of the underlying manifold. Constant curvature metrics on surfaces are such canonical metrics. Their distinguished role is emphasized by classical uniformization theory. Amorerecentcharacterizationofthesemetrics describes them ascriticalpoints of the determinant functional for the Laplacian.The key tool here is Polyakov'sva- ationalformula for the determinant. In higher dimensions, however,it is necessary to further restrict the problem, for instance, to the search for canonical metrics in conformal classes. Here two metrics are considered to belong to the same conf- mal class if they di?er by a nowhere vanishing factor. A typical question in that direction is the Yamabe problem ([165]), which asks for constant scalar curvature metrics in conformal classes. In connection with the problem of understanding the structure of Polyakov type formulas for the determinants of conformally covariant di?erential operators in higher dimensions, Branson ([31]) discovered a remarkable curvature quantity which now is called Branson's Q-curvature. It is one of the main objects in this book.

General

Imprint:	Birkhauser Verlag AG
Country of origin:	Switzerland
Series:	Progress in Mathematics, 275
Release date:	May 2009
First published:	2009
Authors:	Andreas Juhl
Dimensions:	235 x 155 x 30mm (L x W x T)
Format:	Hardcover
Pages:	490
Edition:	2009 ed.
ISBN-13:	978-3-7643-9899-6
Categories:	Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry Promotions
LSN:	3-7643-9899-X
Barcode:	9783764398996

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