2007/12/18 by Ricardo Sá Earp, Earp, Ricardo Sa, Éric Toubiana +1 · 1 citation
Computer Science · Mathematics · #53C42 #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.0712.2972
openalex publication_date 2007/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we prove a general and sharp Asymptotic Theorem for minimal surfaces in H2× R. As a consequence, we prove that there is no properly immersed minimal surface whose asymptotic boundary C is a Jordan curve homologous to zero in the asymptotic boundary of H2× R, say ∂_∞ H2× R, such that C is contained in a slab between two horizontal circles of ∂_∞ H2× R with width equal to π. We construct minimal vertical graphs in H2× R over certain unbounded admissible domains taking certain prescribed finite boundary data and certain prescribed asymptotic boundary data. Our admissible unbounded domains \Om in H2× \0\ are non necessarily convex and non necessarily bounded by convex arcs; each component of its boundary is properly embedded with zero, one or two points on its asymptotic boundary, satisfying a further geometric condition.