Super-potentials for currents on compact Kähler manifolds and dynamics of automorphisms

Dinh, Tien-Cuong; Sibony, Nessim

doi:10.1090/S1056-3911-10-00549-7

Authors: Tien-Cuong Dinh and Nessim Sibony
Journal: J. Algebraic Geom. 19 (2010), 473-529
DOI: https://doi.org/10.1090/S1056-3911-10-00549-7
Published electronically: March 8, 2010
MathSciNet review: 2629598
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Abstract | References | Additional Information

Abstract: We introduce a notion of super-potential (canonical function) associated to positive closed $(p,p)$-currents on compact Kähler manifolds and we develop a calculus on such currents. One of the key points in our study is the use of deformations in the space of currents. As an application, we obtain several results on the dynamics of holomorphic automorphisms: regularity and uniqueness of the Green currents. We also get regularity, entropy, ergodicity and hyperbolicity of the equilibrium measures.

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Additional Information

Tien-Cuong Dinh
Affiliation: UPMC Univ Paris 06, UMR 7586, Institut de Mathématiques de Jussieu, F-75005 Paris, France
MR Author ID: 608547
Email: dinh@math.jussieu.fr

Nessim Sibony
Affiliation: Université Paris-Sud 11, Mathématique - Bâtiment 425, 91405 Orsay, France
MR Author ID: 161495
Email: nessim.sibony@math.u-psud.fr

Received by editor(s): May 12, 2008
Received by editor(s) in revised form: November 4, 2009
Published electronically: March 8, 2010