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Properly Embedded Least Area Planes in Gromov Hyperbolic 3-Spaces

Baris Coskunuzer
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Abstract

We show that for any simple closed curve in the sphere at infinity of a Gromov hyperbolic 3-space with cocompact metric, there exist a properly embedded least area plane in the space spanning the given curve. This gives a positive answer to a conjecture of Gabai. Soma has already proven this conjecture earlier. Our technique here is simpler and more general, and it can be applied to many similar settings.

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Baris Coskunuzer. 2006-09-05. Properly Embedded Least Area Planes in Gromov Hyperbolic 3-Spaces. https://arxiv.org/abs/math/0609099

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