Author: Andreas Juhl
Publisher: Birkhäuser Basel
Keywords: holography, progress, mathematics, curvature, operators, conformally, covariant, differential, families
Number of Pages: 488
Published: 2009-06-26
List price: $119.00
ISBN-10: 376439899X
ISBN-13: 9783764398996

The central object of the book is Q-curvature. This important and subtle scalar Riemannian curvature quantity was introduced by Tom Branson about 15 year ago in connection with variational formulas for determinants of conformally covariant differential operators. The book studies structural properties of Q-curvature from an extrinsic point of view by regarding it as a derived quantity of certain conformally covariant families of differential operators which are associated to hypersurfaces. The new approach is at the cutting edge of central developments in conformal differential geometry in the

Author: John M. Lee
Publisher: American Mathematical Society
Keywords: memoirs, american, mathematical, society, manifolds, compact, operators, einstein, metrics, conformally, fredholm
Number of Pages: 83
Published: 2006-08-09
List price: $55.00
ISBN-10: 0821839152
ISBN-13: 9780821839157

The main purpose of this monograph is to give an elementary and self-contained account of the existence of asymptotically hyperbolic Einstein metrics with prescribed conformal infinities sufficiently close to that of a given asymptotically hyperbolic Einstein metric with nonpositive curvature. The proof is based on an elementary derivation of sharp Fredholm theorems for self-adjoint geometric linear elliptic operators on asymptotically hyperbolic manifolds.