Osaka Journal of Mathematics

On $H = 1/2$ surfaces in $\widetilde{\mathit {PSL}}_{2}(\mathbb {R}, \tau )$

Carlos Peñafiel

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Abstract

In this paper we prove that if $\Sigma$ is a properly embedded constant mean curvature $H = 1/2$ surface which is asymptotic to a horocylinder $C \subset \widetilde{\mathit{PSL}}_{2}(\mathbb{R}, \tau)$, in one side of $C$, such that the mean curvature vector of $\Sigma$ has the same direction as that of the $C$ at points of $\Sigma$ converging to $C$, then $\Sigma$ is a subset of $C$.

Article information

Source
Osaka J. Math., Volume 52, Number 4 (2015), 947-959.

Dates
First available in Project Euclid: 18 November 2015

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1447856027

Mathematical Reviews number (MathSciNet)
MR3426623

Zentralblatt MATH identifier
1336.53069

Subjects
Primary: 53A35: Non-Euclidean differential geometry
Secondary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]

Citation

Peñafiel, Carlos. On $H = 1/2$ surfaces in $\widetilde{\mathit {PSL}}_{2}(\mathbb {R}, \tau )$. Osaka J. Math. 52 (2015), no. 4, 947--959. https://projecteuclid.org/euclid.ojm/1447856027


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