Unique Continuation for Area Minimizing Currents
Abstract
Abstract The main goal of this work is to prove an instance of the unique continuation principle for area minimizing integral currents. More precisely, we consider an m -dimensional area minimizing integral current and an m -dimensional minimal surface, both contained in $${\mathbb {R}}^{n+m}$$ R n + m with $$n\ge 1$$ n ≥ 1 . We show that if, in an integral sense, the current has an infinite order of contact with the minimal surface at a point, then the current and the minimal surface coincide in a neighbourhood of that point.
Fields of Study & Subjects
Electromagnetic Scattering and Analysis
Low-power high-performance VLSI design
Optimization and Search Problems
Publication details
- Journal / source
- Archive for Rational Mechanics and Analysis
- Publisher
- Springer Science and Business Media LLC
- Volume
- 250
- Issue
- 3
- Publication date
- 24 May 2026
- Language
- EN