期刊
JOURNAL OF FUNCTIONAL ANALYSIS
卷 255, 期 9, 页码 2641-2660出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jfa.2007.10.009
关键词
Energy functionals; Kahler-Einstein manifolds; Moser-Trudinger-Onofri inequality
类别
We prove that the existence of a Kahier-Einstein metric on a Fano manifold is equivalent to the properness of the energy functionals defined by Bando, Chen, Ding, Mabuchi and Tian on the set of Kahler metrics with positive Ricci curvature. We also prove that these energy functionals are bounded from below on this set if and only if one of them is. This answers two questions raised by X.-X. Chen. As an application, we obtain a new proof of the classical Moser-Trudinger-Onofri inequality on the two-sphere, as well as describe a canonical enlargement of the space of Kahler potentials on which this inequality holds on higher-dimensional Fano Kahler-Einstein manifolds. (C) 2007 Elsevier Inc. All rights reserved.
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