Generic uniqueness of least area planes in hyperbolic space

Coskunuzer, Baris¹

¹ Department of Mathematics, Yale University, New Haven CT 06520, USA

Geometry & topology, Tome 10 (2006) no. 1, pp. 401-412.

Résumé

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 ${ℍ}^3$.

Détail

DOI : 10.2140/gt.2006.10.401

Keywords: least area plane, asymptotic Plateau problem

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