Article
Energy functionals and canonical Kahler metrics
Duke Mathematical Journal (Impact Factor: 1.7). 06/2005; DOI: 10.1215/S0012709407137153
Source: arXiv

Article: Ricci iterations on Kähler classes
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ABSTRACT: In this paper we consider the dynamical system involved by the Ricci operator on the space of Kähler metrics. A. Nadel has defined an iteration scheme given by the Ricci operator for Fano manifold and asked whether it has some nontrivial periodic points. First, we prove that no such periodic points can exist. We define the inverse of the Ricci operator and consider the dynamical behaviour of its iterates for a Fano KählerEinstein manifold. In particular we show that the iterates do converge to the KählerRicci soliton for toric manifolds. Finally, we define a finite dimensional procedure to give an approximation of KählerEinstein metrics using this iterative procedure and apply it for P 2 blown up in 3 points.Journal of the Institute of Mathematics of Jussieu 10/2007; 8(04). · 1.02 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Using Perelman's results on KählerRicci flow, we prove that the $K$energy is bounded from below if and only if the $F$functional is bounded from below in the canonical Kähler class.OSAKA JOURNAL OF MATHEMATICS 03/2008; 45(1). · 0.37 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We prove the conjecture of Tian on the strong form of the MoserTrudinger inequality for KÃ¤hlerEinstein manifolds with positive first Chern class, when there are no holomorphic vector fields, and, more generally, when the setting is invariant under a maximal compact subgroup of the automorphism group.American Journal of Mathematics 01/2008; · 1.35 Impact Factor
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