Complex projective structures: Lyapunov exponent, degree, and harmonic measure

DOI10.1215/00127094-2017-0012zbMath1381.57013arXiv1308.0541OpenAlexW3105765050MaRDI QIDQ1676346

Bertrand Deroin, Romain Dujardin

Publication date: 6 November 2017

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.0541

zbMATH Keywords

Brownian motionharmonic measureLyapunov exponentKleinian groupscovering degreecomplex projective structures

Mathematics Subject Classification ID

Klein surfaces (30F50) Value distribution of meromorphic functions of one complex variable, Nevanlinna theory (30D35) Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) General geometric structures on low-dimensional manifolds (57M50) Capacity and harmonic measure in the complex plane (30C85) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40)

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Singularities for analytic continuations of holonomy germs of Riccati foliations ⋮ A Fatou theorem for \(F\)-harmonic functions ⋮ Heijal's theorem for projective structures on surfaces with parabolic punctures ⋮ Pluripotential theory on Teichmüller space. II: Poisson integral formula ⋮ Analytic continuation of holonomy germs of Riccati foliations along Brownian paths ⋮ Lyapunov exponents, holomorphic flat bundles and de Rham moduli space ⋮ Lyapunov exponents for surface group representations ⋮ Lower bounds for Lyapunov exponents of flat bundles on curves ⋮ Teichmüller Theory, Thurston Theory, Extremal Length Geometry and Complex Analysis ⋮ On the dynamics of Riccati foliations with nonparabolic monodromy representations

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