scholarly journals Fredholm operators and Einstein metrics on conformally compact manifolds

2006 ◽  
Vol 183 (864) ◽  
pp. 0-0 ◽  
Author(s):  
John M. Lee
Keyword(s):  
Einstein Metrics ◽  
Compact Manifolds ◽  
Fredholm Operators ◽  
Conformally Compact

scholarly journals Dynamics and Zeta functions on conformally compact manifolds

2014 ◽  
Vol 367 (4) ◽  
pp. 2459-2486
Author(s):  
Julie Rowlett ◽  
Pablo Suárez-Serrato ◽  
Samuel Tapie
Keyword(s):  
Zeta Functions ◽  
Compact Manifolds ◽  
Conformally Compact

Affine compact almost-homogeneous manifolds of cohomogeneity one

2009 ◽  
Vol 7 (1) ◽  
Author(s):  
Daniel Guan
Keyword(s):  
Einstein Metrics ◽  
Compact Manifolds ◽  
Complex Manifolds ◽  
Homogeneous Manifolds ◽  
Einstein Manifolds ◽  
Extremal Metrics ◽  
Cohomogeneity One ◽  
Fano Manifolds ◽  
Kähler Einstein Metrics

AbstractThis paper is one in a series generalizing our results in [12, 14, 15, 20] on the existence of extremal metrics to the general almost-homogeneous manifolds of cohomogeneity one. In this paper, we consider the affine cases with hypersurface ends. In particular, we study the existence of Kähler-Einstein metrics on these manifolds and obtain new Kähler-Einstein manifolds as well as Fano manifolds without Kähler-Einstein metrics. As a consequence of our study, we also give a solution to the problem posted by Ahiezer on the nonhomogeneity of compact almost-homogeneous manifolds of cohomogeneity one; this clarifies the classification of these manifolds as complex manifolds. We also consider Fano properties of the affine compact manifolds.

scholarly journals Boundary regularity of conformally compact Einstein metrics

2005 ◽  
Vol 69 (1) ◽  
pp. 111-136 ◽  
Author(s):  
Piotr T. Chruściel ◽  
Erwann Delay ◽  
John M. Lee ◽  
Dale N. Skinner
Keyword(s):  
Einstein Metrics ◽  
Boundary Regularity ◽  
Conformally Compact

PROOF OF THE RIGIDITY OF HYPERBOLIC SPACES USING QUASILOCAL MASS TYPE THEOREMS

2005 ◽  
Vol 02 (02) ◽  
pp. 471-479
Author(s):  
PENGZI MIAO
Keyword(s):  
General Relativity ◽  
Hyperbolic Spaces ◽  
Compact Manifolds ◽  
Standard Sphere ◽  
Conformally Compact ◽  
Quasilocal Mass ◽  
Mass Type

A proof of the rigidity of hyperbolic spaces is given for a class of conformally compact manifolds whose conformal infinity is the standard sphere. The method is based on quasilocal mass type theorems in general relativity.

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