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- Title
Nonproper Complete Minimal Surfaces Embedded in H<sup>2</sup> × R.
- Authors
Rodríguez, Magdalena; Tinaglia, Giuseppe
- Abstract
Examples of complete minimal surfaces properly embedded in H2 × R have been extensively studied and the literature contains a plethora of nontrivial ones. In this paper, we construct a large class of examples of complete minimal surfaces embedded in H2 × R, not necessarily proper, which are invariant by a vertical translation or by a screw motion. In particular, we construct a large family of nonproper complete minimal disks embedded in H2 × R invariant by a vertical translation and a screw motion and whose importance is two-fold. They have finite total curvature in the quotient of H2 × R by the isometry, thus highlighting a very different behavior from minimal surfaces embedded in R3 satisfying the same properties. They show that the Calabi-Yau conjectures for embedded minimal surfaces do not hold in H2 × R.
- Subjects
MINIMAL surfaces; GRAPH theory; EMBEDDINGS (Mathematics); GAUSS-Bonnet theorem; BOUNDARY value problems; MAXIMUM principles (Mathematics)
- Publication
IMRN: International Mathematics Research Notices, 2015, Issue 12, p4322
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnu068