Heat equation and ergodic theorems for Riemann surface laminations

DOI10.1007/s00208-011-0730-8zbMath1331.37064arXiv1004.3931OpenAlexW1637441234MaRDI QIDQ453325

Nessim Sibony, Tien-Cuong Dinh, Viêt-Anh Nguyên

Publication date: 19 September 2012

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.3931

zbMATH Keywords

singular foliationsharmonic currents

Mathematics Subject Classification ID

Ergodic theory (37A99) Dynamical aspects of holomorphic foliations and vector fields (37F75) Integration on analytic sets and spaces, currents (32C30)

Related Items (18)

Oseledec multiplicative ergodic theorem for laminations ⋮ Singular holomorphic foliations by curves. I: Integrability of holonomy cocycle in dimension 2 ⋮ The second main theorem in the hyperbolic case ⋮ Geometric characterization of Lyapunov exponents for Riemann surface laminations ⋮ Poincaré metric of holomorphic foliations with non-degenerate singularities ⋮ Relatively uniformly continuous semigroups on vector lattices ⋮ 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 ⋮ Heat diffusions on holomorphic foliations with non-degenerate singularities ⋮ Singular holomorphic foliations by curves. II: Negative Lyapunov exponent ⋮ On the work of Sarig on countable Markov chains and thermodynamic formalism ⋮ Some open problems on holomorphic foliation theory ⋮ Pfaff systems, currents and hulls ⋮ Ergodic theorems for laminations and foliations: recent results and perspectives ⋮ Directed harmonic currents near hyperbolic singularities ⋮ Unique ergodicity for foliations on compact Kähler surfaces

Cites Work

• Foliations, the ergodic theorem and Brownian motion
• Examples of minimal laminations and associated currents
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• The harmonic measures of Lucy Garnett
• The \(\overline\partial\)-equation on a positive current
• Uniformization of the leaves of a rational vector field
• Unique ergodicity of harmonic currents on singular foliations of \({\mathbb{P}^2}\)
• Inexistence of invariant measures for generic rational differential equations in the complex domain
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• [https://portal.mardi4nfdi.de/wiki/Publication:2710399 Uniformization and the Poincar� metric on the leaves of a foliation by curves]
• Uniformization of surface laminations
• An Operator Theorem on $L_1$ Convergence to Zero with Applications to Markov Kernels
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