Unique ergodicity for foliations on compact ...
Document type :
Compte-rendu et recension critique d'ouvrage
Title :
Unique ergodicity for foliations on compact Kähler surfaces
Author(s) :
Dinh, Tien-Cuong [Auteur]
National University of Singapore [NUS]
Nguyên, Viêt-Anh [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Sibony, Nessim [Auteur]
Université Paris-Saclay
National University of Singapore [NUS]
Nguyên, Viêt-Anh [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Sibony, Nessim [Auteur]
Université Paris-Saclay
Journal title :
Duke Mathematical Journal
Publisher :
Duke University Press
Publication date :
2022-01-01
ISSN :
0012-7094
HAL domain(s) :
Mathématiques [math]
English abstract : [en]
Let F be a holomorphic foliation by Riemann surfaces on a compact Kähler surface X . Assume that it is generic in the sense that all the singularities are hyperbolic, and the foliation admits no directed positive closed ...
Show more >Let F be a holomorphic foliation by Riemann surfaces on a compact Kähler surface X . Assume that it is generic in the sense that all the singularities are hyperbolic, and the foliation admits no directed positive closed .1; 1/-current. Then there existsa unique (up to a multiplicative constant) positive d d c -closed .1; 1/-current directed by F . This is a very strong ergodic property of F showing that all leaves of F have the same asymptotic behavior. Our proof uses an extension of the theory of densities to a class of non-d d c -closed currents. This is independent of foliation theory and represents a new tool in pluripotential theory. A complete description of the cone of directed positive ddc -closed .(1,1)-currents is also given when F admits directed positive closed currents.Show less >
Show more >Let F be a holomorphic foliation by Riemann surfaces on a compact Kähler surface X . Assume that it is generic in the sense that all the singularities are hyperbolic, and the foliation admits no directed positive closed .1; 1/-current. Then there existsa unique (up to a multiplicative constant) positive d d c -closed .1; 1/-current directed by F . This is a very strong ergodic property of F showing that all leaves of F have the same asymptotic behavior. Our proof uses an extension of the theory of densities to a class of non-d d c -closed currents. This is independent of foliation theory and represents a new tool in pluripotential theory. A complete description of the cone of directed positive ddc -closed .(1,1)-currents is also given when F admits directed positive closed currents.Show less >
Language :
Anglais
Popular science :
Non
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