Number of least area planes in Gromov hyperbolic 3-spaces. (English) Zbl 1196.53007
The author has a multitude of remarkable results in the field of Plateau problems in hyperbolic spaces, involving existence and uniqueness problems, area-minimizing surfaces, and related topics. In this specific paper, he shows that, given a simple closed curve in the asymptotic boundary of a Gromov hyperbolic 3-space with cocompact metric, there exists a UNIQUE least area plane (with respect to the metric).
Reviewer: Magdalena Daniela Toda (Lubbock)
MSC:
| 53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |
| 57M50 | General geometric structures on low-dimensional manifolds |
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