Compact complete proper minimal immersions in strictly convex bounded regular domains of R³

2008/04/30 by Antonio Alarcón, Alarcon, Antonio
Mathematics · #49Q05 #49Q10 #53A10 #53C42 #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.0804.4778

openalex publication_date 2008/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider a strictly convex bounded regular domain C of \R³. For any arbitrary finite topological type we find a compact Riemann surface M, an open domain M⊂ M with the fixed topological type, and a conformal complete proper minimal immersion X:M→ C which can be extended to a continuous map X:M→ C.

Related

• Existence of proper minimal surfaces of arbitrary topological type
• Compact complete minimal immersions in R³
• Complete proper minimal surfaces in convex bodies of ℝ³ (II): The behavior of the limit set
• Limit sets for complete minimal immersions
• Complete proper minimal surfaces in convex bodies of R³