Unique ergodicity of harmonic currents on singular foliations of \({\mathbb{P}^2}\)

DOI10.1007/s00039-009-0043-1zbMath1204.32022arXivmath/0606744OpenAlexW1768318944MaRDI QIDQ2269896

Nessim Sibony, John-Erik Fornaess

Publication date: 12 March 2010

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0606744

zbMATH Keywords

holomorphic foliationsharmonic measureshyperbolic singularitiesminimal exceptional set

Mathematics Subject Classification ID

Harmonic functions on Riemann surfaces (30F15) Singularities of holomorphic vector fields and foliations (32S65) Foliations in differential topology; geometric theory (57R30) Currents (32U40)

Related Items (20)

Oseledec multiplicative ergodic theorem for laminations ⋮ Singular holomorphic foliations by curves. I: Integrability of holonomy cocycle in dimension 2 ⋮ Topology and complex structures of leaves of foliations by Riemann surfaces ⋮ Directed harmonic currents near non-hyperbolic linearizable singularities ⋮ Unique ergodicity for foliations in \(\mathbb {P}^2\) with an invariant curve ⋮ Leafwise Brownian motions and some function theoretic properties of laminations ⋮ Singular holomorphic foliations by curves. III: Zero Lelong numbers ⋮ Singular holomorphic foliations by curves. II: Negative Lyapunov exponent ⋮ Convexity of complements of limit sets for holomorphic foliations on surfaces ⋮ Ergodicity of laminations with singularities in Kähler surfaces ⋮ Examples of minimal laminations and associated currents ⋮ Heat equation and ergodic theorems for Riemann surface laminations ⋮ Uniformizing complex ODEs and applications ⋮ On the work of Sarig on countable Markov chains and thermodynamic formalism ⋮ Riemann surface laminations with singularities ⋮ Ergodic theorems for laminations and foliations: recent results and perspectives ⋮ Directed harmonic currents near hyperbolic singularities ⋮ Harmonic currents directed by foliations by Riemann surfaces ⋮ Unique ergodicity for foliations on compact Kähler surfaces ⋮ On the dynamics of Riccati foliations with nonparabolic monodromy representations

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