#### Volume 10, issue 1 (2006)

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Generic uniqueness of least area planes in hyperbolic space

### Baris Coskunuzer

Geometry & Topology 10 (2006) 401–412
 arXiv: math.GT/0408066
##### Abstract

We study the number of solutions of the asymptotic Plateau problem in ${ℍ}^{3}$. By using the analytical results in our previous paper, and some topological arguments, we show that there exists an open dense subset of ${C}^{3}$ Jordan curves in ${S}_{\infty }^{2}\left({ℍ}^{3}\right)$ such that any curve in this set bounds a unique least area plane in ${ℍ}^{3}$.

##### Keywords
least area plane, asymptotic Plateau problem
Primary: 53A10
Secondary: 58B15