2013/12/12 by Xiangyu Liang, Liang, Xiangyu
Computer Science · Mathematics · #28A75 #49K99 #49Q20 #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #math.CA #msc:28A75 #msc:49K99 #msc:49Q20
paper · pdf · doi:10.48550/arxiv.1312.3489
44 pages. arXiv admin note: substantial text overlap with arXiv:1103.1468
arxiv created 2013/12/12 · openalex publication_date 2013/12/12 · arxiv updated 2013/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we prove the topological minimality of unions of several almost orthogonal planes of arbitrary dimensions. A particular case was proved in arXiv:1103.1468, where we proved the Almgren minimality (which is a weaker property than the topological minimality) of the union of two almost orthogonal 2 dimensional planes. On the one hand, the topological minimality is always proved by variations of calibration methods, but in this article, we give a continuous family topological minimal sets, hence calibrations cannot apply. The advantage of a set being topological minimal (compared to Almgren minimal) is that its product with \Rn stays topological minimal. This leads also to finding minimal sets which are unions of non transversal (hence far from almost orthogonal) planes; On the other hand, regularity for higher dimensional minimal sets is much less clear than those of dimension 2, hence more efforts are needed for higher dimensional cases.