Overview
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.
Full Product Details
Author: Andreas Juhl
Publisher: Birkhauser Verlag AG
Imprint: Birkhauser Verlag AG
Edition: 2009 ed.
Volume: 275
Dimensions:
Width: 15.50cm
, Height: 3.00cm
, Length: 23.50cm
Weight: 1.000kg
ISBN: 9783764398996
ISBN 10: 376439899
Pages: 490
Publication Date: 13 May 2009
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Hardback
Publisher's Status: Active
Availability: In Print
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Reviews
"From the reviews: ""The author focuses this book on the ! Q-curvature and its relations with the conformal differential geometry. ! This beautiful and interesting research book covers a new topic in Riemannian differential geometry that intersects many areas of the actual research in Mathematics and in Mathematical Physics. Thus it can be highly recommended to all Mathematicians ! ."" (Agostino Prastaro, Zentralblatt MATH, Vol. 1177, 2010)"
From the reviews: The author focuses this book on the ! Q-curvature and its relations with the conformal differential geometry. ! This beautiful and interesting research book covers a new topic in Riemannian differential geometry that intersects many areas of the actual research in Mathematics and in Mathematical Physics. Thus it can be highly recommended to all Mathematicians ! . (Agostino Prastaro, Zentralblatt MATH, Vol. 1177, 2010)
From the reviews: The author focuses this book on the ! Q-curvature and its relations with the conformal differential geometry. ! This beautiful and interesting research book covers a new topic in Riemannian differential geometry that intersects many areas of the actual research in Mathematics and in Mathematical Physics. Thus it can be highly recommended to all Mathematicians ! . (Agostino Prastaro, Zentralblatt MATH, Vol. 1177, 2010)
From the reviews: The author focuses this book on the ... Q-curvature and its relations with the conformal differential geometry. ... This beautiful and interesting research book covers a new topic in Riemannian differential geometry that intersects many areas of the actual research in Mathematics and in Mathematical Physics. Thus it can be highly recommended to all Mathematicians ... . (Agostino Prastaro, Zentralblatt MATH, Vol. 1177, 2010)
