New complete embedded minimal surfaces in H2xR

Details New complete embedded minimal surfaces in H2xR New complete embedded minimal surfaces in H2xR

2009-11-30

arxiv.org/abs/0911.5577v2

Mathematics

Differential Geometry

3 figures, corrected typos

Scientific paper

We construct three kinds of complete embedded minimal surfaces in $\Bbb H^2\times \Bbb R$. The first is a simply connected, singly periodic, infinite total curvature surface. The second is an annular finite total curvature surface. These two are conjugate surfaces just as the helicoid and the catenoid are in $\mathbb R^3$. The third one is a finite total curvature surface which is conformal to $\mathbb S^2\setminus\{p_1,...,p_k\}, k\geq3.$

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