Unique tangent behavior for 1-dimensional stationary varifolds

TL;DR

This paper proves that 1-dimensional stationary varifolds in any Riemannian manifold have a unique tangent behavior at every point, regardless of density bounds or codimension assumptions.

Contribution

It establishes the uniqueness of tangent cones for 1-dimensional stationary varifolds without additional density or codimension restrictions.

Findings

Unique tangent behavior at all points for 1-dimensional stationary varifolds

No assumptions on lower density bounds or codimension needed

Applicable to any Riemannian manifold

Abstract

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 everywhere.