Regularity for minimal sets near a union of two planes

2012/03/02 by Xiangyu Liang, Liang, Xiangyu
Computer Science · Mathematics · #28A75 #49K99 #49Q10 #49Q20 #Advanced Differential Equations and Dynamical Systems #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Point processes and geometric inequalities #math.CA #msc:28A75 #msc:49K99 #msc:49Q10 #msc:49Q20

paper · pdf · doi:10.48550/arxiv.1203.0560

30 pages. arXiv admin note: substantial text overlap with arXiv:1112.3565

openalex publication_date 2012/03/02 · arxiv created 2012/05/13 · arxiv updated 2012/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the global regularity of 2 dimensional minimal sets that are near a union of two planes, and prove that every global minimal set in R⁴ that looks like a union of two almost orthogonal planes at infinity is a cone. The main point is to use the topological properties of a minimal set at a large scale to control its behavior at smaller scales.

Citations

• Global regularity for minimal sets near a \T set and counterexamples

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• On the topological minimality of unions of planes of arbitrary dimension
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