Unique continuation for area minimizing currents

Abstract

The main goal of this work is to prove an instance of the unique continuation principle for area minimizing integral currents. More precisely, consider an $m$-dimensional area minimizing integral current and an $m$-dimensional minimal surface, both contained in $\mathbb{R}^{n+m}$ with $n\geq 1$. We show that if, in an integral sense, the current has infinite order of contact with the minimal surface at a point, then the current and the minimal surface coincide in a neighborhood of that point.