Number of Least Area Planes in Gromov Hyperbolic 3-Spaces

Details Number of Least Area Planes in Gromov Hyperbolic 3-Spaces Number of Least Area Planes in Gromov Hyperbolic 3-Spaces

2008-05-14

arxiv.org/abs/0805.1978v1

Proc. Amer. Math. Soc. 138 (2010) 2923-2937.

Mathematics

Geometric Topology

Scientific paper

10.1090/S0002-9939-10-10308-6

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

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