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arXiv · 1808.09687

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

Xiangyu Liang
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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..

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Xiangyu Liang. 2018-08-29. Minimality for unions of 2-dimensional minimal cones with non-isolated singularities. https://arxiv.org/abs/1808.09687

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