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arXiv · 1101.3843

Non-properly Embedded Minimal Planes in Hyperbolic 3-Space

Baris Coskunuzer
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Abstract

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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BibTeXRIS

Baris Coskunuzer. 2011-01-20. Non-properly Embedded Minimal Planes in Hyperbolic 3-Space. https://doi.org/10.1142/s0219199711004415

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