9 citations · 25 across the 10 of their papers we have counts for
10 papers · 1 filter
Unique tangent behavior for 1-dimensional stationary varifolds
Xiangyu Liang
We prove that, without any assumption on lower density bound or codimension, any 1-dimensional stationary varifold on any Riemannian manifold admits unique tangent behaviour everyw…
Uniqueness of 2-dimensional minimal cones in
Xiangyu Liang
In this article we treat two closely related problems: 1) the upper semi continuity property for Almgren minimal sets in regions with regular boundary, which guanrantees that the u…
Measure and sliding stability for 2-dimensional minimal cones in Euclidean spaces
Xiangyu Liang
In this article we prove the measure stability for all 2-dimensional Almgren minimal cones in , and the Almgren (resp. topological) sliding stability for the 2-dimens…
Minimality for unions of 2-dimensional minimal cones with non-isolated singularities
Xiangyu Liang
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 t…
Limits of topological minimal sets with finitely generated coefficient groups
Xiangyu Liang
We prove that Hausdorff limit of topological minimal sets (with finitely generated coefficient group) are topologically minimal. The key idea is to reduce the homology group on the…
On the topological minimality of unions of planes of arbitrary dimension
Xiangyu Liang
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…