Minimality for unions of 2-dimensional minimal cones with non-isolated singularities

Abstract

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 \cite{2p,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..

arXiv comment78 pages

References in corpus (2)

• Existence of solutions to a general geometric elliptic variational problem
• Measure and sliding stability for 2-dimensional minimal cones in Euclidean spaces

Cited by in corpus (2)

• Measure and sliding stability for 2-dimensional minimal cones in Euclidean spaces
• Uniqueness of 2-dimensional minimal cones in ${\mathbb{R}}^3$