NON-PROPERLY EMBEDDED MINIMAL PLANES IN HYPERBOLIC 3-SPACE-Reference-Cited by-同舟云学术

NON-PROPERLY EMBEDDED MINIMAL PLANES IN HYPERBOLIC 3-SPACE

Published:2011-10 Issue:05 Volume:13 Page:727-739
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

COSKUNUZER BARIS¹

Affiliation:

1. Department of Mathematics, Koc University, Sariyer, Istanbul 34450, Turkey

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 non-positive curvature. We show this result by constructing a non-properly embedded minimal plane in H3. Hence, this gives a counterexample to Calabi–Yau conjecture for embedded minimal surfaces in negative curvature case.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199711004415

Reference10 articles.

1. The Calabi–Yau conjectures for embedded surfaces

2. Least area planes in hyperbolic $3$-space are properly embedded

3. On the geometric and topological rigidity of hyperbolic 3-manifolds

4. Intersections of least area surfaces

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