Published Paper

Inserted: 10 aug 2023
Last Updated: 28 sep 2026

Journal: Inventiones Mathematicae
Year: 2023

Abstract:

We prove that if $u : B_1 \subset \mathbb{R}^2 \rightarrow \mathbb{R}^n$ is a Lipschitz critical point of the area functional with respect to outer variations, then $u$ is smooth. This solves a conjecture of Lawson and Osserman from 1977 in the planar case.