Limit sets for complete minimal immersions

2006/12/06 by A. Alarcon, Antonio Alarcón, N. Nadirashvili +3
Computer Science · Engineering · Mathematics · #49Q05 #49Q10 #53A10 #53C42 #Advanced Numerical Analysis Techniques #Advanced Topology and Set Theory #Differential Geometry (math.DG) #FOS: Mathematics #Optimization and Variational Analysis #math.DG #msc:49Q05 #msc:49Q10 #msc:53A10 #msc:53C42

paper · pdf · doi:10.48550/arxiv.math/0612149

8 pages, 3 figures. To appear in Math. Z

openalex publication_date 2006/12/06 · arxiv created 2007/02/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the behaviour of the limit set of complete proper compact minimal immersions in a regular domain G of R³. We prove that the second fundamental form of the boundary surface of G is nonnegatively defined at every point of the limit set of such immersions.

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