2011/03/20 by Xiangyu Liang, Liang, Xiangyu · 1 citation
Computer Science · Engineering · Mathematics · #28A75 #49K99 #49Q20 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Analysis Techniques #Classical Analysis and ODEs (math.CA) #Elasticity and Material Modeling #FOS: Mathematics #math.CA #msc:28A75 #msc:49K99 #msc:49Q20
paper · pdf · doi:10.48550/arxiv.1103.3871
arxiv created 2011/03/20 · openalex publication_date 2011/03/20 · arxiv updated 2011/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we introduce a definition of topological minimal sets, which is a generalization of that of Mumford-Shah-minimal sets. We prove some general properties as well as two existence theorems for topological minimal sets. As an application we prove the topological minimality of the union of two almost orthogonal planes in \R4, and use it to improve the angle criterion under which the union of several higher dimensional planes is Almgren-minimal.