Families of Conformally Covariant Differential Operators, Q-Curvature and Holography (275) - Couverture rigide

Juhl, Andreas

Couverture rigide

ISBN 10 : 376439899X ISBN 13 : 9783764398996

Editeur : Birkhauser Verlag AG, 2009

Synopsis

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.

Détails de l'édition

• Éditeur: Birkhauser Verlag AG
• Date d'édition: 2009
• Langue: anglais
• ISBN 10: 376439899X
• ISBN 13: 9783764398996
• Reliure: Relié
• Nombre de pages: 490
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible