Publication: Number of least area planes in gromov hyperbolic 3-spaces
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Abstract
We show that for a generic simple closed curve Gamma in the asymptotic boundary of a Gromov hyperbolic 3-space with cocompact metric X, there exists a unique least area plane Sigma in X such that partial derivative(infinity)Sigma = Gamma. This result has interesting topological applications for constructions of canonical 2-dimensional objects in Gromov hyperbolic 3-manifolds.
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American Mathematical Society (AMS)
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Least area planes hyperbolic space, Cocompact metric space geometry, Gromov hyperbolic space
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Proceedings of The American Mathematical Society
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10.1090/S0002-9939-10-10308-6
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