Non-properly Embedded Minimal Planes in Hyperbolic 3-Space

Details Non-properly Embedded Minimal Planes in Hyperbolic 3-Space Non-properly Embedded Minimal Planes in Hyperbolic 3-Space

2011-01-20

arxiv.org/abs/1101.3843v1

Comm. Contemp. Math. 13 (2011) 727-739

Mathematics

Differential Geometry

Scientific paper

10.1142/S0219199711004415

In this paper, we show that there are non-properly embedded minimal surfaces with finite topology in a simply connected Riemannian 3-manifold with nonpositive curvature. We show this result by constructing a non-properly embedded minimal plane in hyperbolic 3-space. Hence, this gives a counterexample to Calabi-Yau conjecture for embedded minimal surfaces in the negative curvature case.

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