TL;DR
This paper addresses the asymptotic Plateau Problem for minimal surfaces in hyperbolic space cross real line, providing a comprehensive characterization of boundary curves that bound minimal surfaces.
Contribution
It offers a near-complete solution to the problem, identifying which Jordan curves in the asymptotic boundary can bound minimal surfaces in H^2xR.
Findings
Characterization of boundary curves bounding minimal surfaces
Identification of the collection of Jordan curves in the asymptotic boundary
Complete solution to the asymptotic Plateau Problem in H^2xR
Abstract
We give a fairly complete solution to the asymptotic Plateau Problem for minimal surfaces in H^2xR. In particular, we identify the collection of finite Jordan curves in the asymptotic cylinder which bounds a minimal surface in H^2xR.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Point processes and geometric inequalities