Asymptotic H–Plateau problem in ℍ3

Coskunuzer, Baris¹

¹ Massachusetts Institute of Technology, Mathematics Department, Cambridge, MA 02139, USA, Department of Mathematics, Koç University, Istanbul 34450, Turkey

Geometry & topology, Tome 20 (2016) no. 1, pp. 613-627.

Résumé

We show that for any Jordan curve $\Gamma$ in $S_{\infty }^2\left({ℍ}^3\right)$ with at least one smooth point, there exists an embedded $H$–plane ${\mathcal{P}}_H$ in ${ℍ}^3$ with ${\partial }_{\infty }{\mathcal{P}}_H=\Gamma$ for any $H\in \left[0,1\right)$.

Détail

DOI : 10.2140/gt.2016.20.613

Classification : 53A10
Keywords: asymptotic Plateau problem, constant mean curvature, $H$–surfaces, hyperbolic space

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