Hyperbolicity properties of quotient surfaces by freely operating arithmetic lattices

Eberhard Oeljeklaus; Christina Schmerling

Displaying similar documents to “Hyperbolicity properties of quotient surfaces by freely operating arithmetic lattices”

Failure of averaging on multiply connected domains

David E. Barrett (1990)

Annales de l'institut Fourier

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We show that for every open Riemann surface $X$ with non-abelian fundamental group there is a multiple-valued function $f$ on $X$ such that the fiberwise convex hull of the graph of $f$ fails to contain the graph of a single-valued holomorphic function on $X$ .

A survey of boundary value problems for bundles over complex spaces

Harris, Adam

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Let $X$ be a reduced $n$ -dimensional complex space, for which the set of singularities consists of finitely many points. If $X^{'} \subseteq X$ denotes the set of smooth points, the author considers a holomorphic vector bundle $E \to X^{'} ∖ A$ , equipped with a Hermitian metric $h$ , where $A$ represents a closed analytic subset of complex codimension at least two. The results, surveyed in this paper, provide criteria for holomorphic extension of $E$ across $A$ , or across the singular points of $X$ if $A = ⌀$ . The approach taken here is...

On holomorphic maps into compact non-Kähler manifolds

Masahide Kato, Noboru Okada (2004)

Annales de l’institut Fourier

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We study the extension problem of holomorphic maps $σ : H \to X$ of a Hartogs domain $H$ with values in a complex manifold $X$ . For compact Kähler manifolds as well as various non-Kähler manifolds, the maximal domain $Ω_{σ}$ of extension for $σ$ over $Δ$ is contained in a subdomain of $Δ$ . For such manifolds, we define, in this paper, an invariant Hex $_{n} (X)$ using the Hausdorff dimensions of the singular sets of $σ$ ’s and study its properties to deduce informations on the complex structure of $X$ .

Determination of the pluripolar hull of graphs of certain holomorphic functions

Armen Edigarian, Jan Wiegerinck (2004)

Annales de l’institut Fourier

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Let $A$ be a closed polar subset of a domain $D$ in $ℂ$ . We give a complete description of the pluripolar hull $Γ_{D \times ℂ}^{*}$ of the graph $Γ$ of a holomorphic function defined on $D ∖ A$ . To achieve this, we prove for pluriharmonic measure certain semi-continuity properties and a localization principle.