Affiliation:
1. School of Mathematics, Beihang University, no. 37 XueYuan Road, Beijing, 100191, P. R. China
Abstract
Abstract
In this article, we prove the translational stability for all two-dimensional Almgren minimal cones in ${\mathbb{R}}^n$ and the Almgren (resp. topological) sliding stability for the two-dimensional Almgren (resp. topological) minimal cones in ${\mathbb{R}}^3$. As proved in [ 19], when several two-dimensional Almgren (resp. topological) minimal cones are translational, Almgren (resp. topological) sliding stable, and Almgren (resp. topological) unique, their almost orthogonal union stays minimal. As a consequence, the results of this article, together with the uniqueness properties proved in [ 14], permit us to use all two-dimensional minimal cones in ${\mathbb{R}}^3$ to generate new families of minimal cones by taking their almost orthogonal unions.
Funder
China’s Recruitement Program of Global Experts, School of Mathematics and Systems Science, Beihang University
National Science Foundation
Publisher
Oxford University Press (OUP)
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