2004/05/26 by Francisco Martín, Francisco Martin, Santiago Morales +2
Mathematics · #49Q10 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #General Mathematics (math.GM) #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Point processes and geometric inequalities #Primary 53A10 #Secondary 49Q05 #math.DG #math.GM #msc:49Q05 #msc:49Q10 #msc:53A10 #msc:53C42
paper · pdf · doi:10.48550/arxiv.math/0405507
26 pages, 7 figures
arxiv created 2004/05/26 · openalex publication_date 2004/05/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a convex domain B of space. We prove that there exist complete minimal surfaces which are properly immersed in B. We also demonstrate that if D and D' are convex domains with D bounded and the closure of D contained in D' then any minimal disk whose boundary lies in the boundary of D, can be approximated in any compact subdomain of D by a complete minimal disk which is proper in D'. We apply these results to study the so called type problem for a minimal surface: we demonstrate that the interior of any convex region is not a universal region for minimal surfaces, in the sense explained by Meeks and Perez.