Singular Holomorphic Foliations by Curves II: Negative Lyapunov Exponent

Nguyen, Viet Anh

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1007/s12220-023-01365-z

Title :

Singular Holomorphic Foliations by Curves II: Negative Lyapunov Exponent

Author(s) :

Nguyen, Viet Anh [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

The Journal of Geometric Analysis

Pages :

315

Publisher :

Springer

Publication date :

2023-07-18

ISSN :

1050-6926

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

Let F be a holomorphic foliation by Riemann surfaces defined on a compact complexprojective surface X satisfying the following two conditions: the singular points of Fare all hyperbolic; F is Brody hyperbolic. Then we ...
Show more >Let F be a holomorphic foliation by Riemann surfaces defined on a compact complexprojective surface X satisfying the following two conditions: the singular points of Fare all hyperbolic; F is Brody hyperbolic. Then we establish cohomological formulasfor the Lyapunov exponent and the Poincaré mass of an extremal positive ddc -closedcurrent tangent to F . If, moreover, there is no nonzero positive closed current tangentto F , then we show that the Lyapunov exponent χ (F ) of F , which is, by definition,the Lyapunov exponent of the unique normalized positive ddc -closed current tangentto F , is a strictly negative real number. As an application, we compute the Lyapunovexponent of a generic foliation with a given degree in P2 .Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions
Quantisation, singularités et dynamique holomorphe

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Files

1812.10125
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