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NUMBER OF LEAST AREA PLANES IN GROMOV HYPERBOLIC

By Baris Coskunuzer

Abstract

ABSTRACT. We show that for a generic simple closed curve Γ in the asymptotic boundary of a Gromov hyperbolic 3-space with cocompact metric X, there exist a unique least area plane Σ in X such that ∂∞Σ = Γ. This result has interesting topological applications for constructions of canonical 2-dimensional objects in 3-manifolds. 1

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