2018/08/29 by Xiangyu Liang, Liang, Xiangyu · 2 citations
Mathematics · #28A75 #49K21 #49K99 #49Q20 #Advanced Banach Space Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Point processes and geometric inequalities #math.CA #msc:28A75 #msc:49K21 #msc:49K99 #msc:49Q20
paper · pdf · doi:10.48550/arxiv.1808.09687
78 pages
arxiv created 2018/08/29 · openalex publication_date 2018/08/29 · arxiv updated 2018/08/30 · openalex created_date 2018/09/07 · openalex updated_date 2026/07/28
In this article we prove that for a large class of 2-dimensional minimal cones (including almost all 2-dimensional minimal cones that we know), the almost orthogonal union of any two of them is still a minimal cone. Comparing to existing results for minimality of almost orthogonal union of planes \cite2p,2ptopo, here we are dealing with unions of cones with non isolated singularities, which results in a series of essential difficulties, and new ideas are required. The proof in this article can be generalized to other types of minimalities, e.g. topological minimality, Reifenberg minimality, etc..