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On the Lawson-Osserman conjecture

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arxiv 2308.04997 v1 pith:2HEHGE3O submitted 2023-08-09 math.AP math.DG

Jonas Hirsch , Connor Mooney , Riccardo Tione This is my paper · ORCID
classification math.APmath.DG
keywords conjecturemathbbareacasecriticalfunctionallawsonlawson-osserman
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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.

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  1. Solutions to the minimal surface system with large singular sets

    math.AP 2024-11 conditional novelty 8.0 of 10

    Minimizing sequences for the area of Lipschitz graphs from R^3 to R^2 can converge to Cartesian currents with large interior vertical, non-minimal patches, in the smallest possible dimension and codimension.

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