On the Lawson-Osserman conjecture

2023/08/09 by Hirsch, Jonas, Mooney, Connor, Tione, Riccardo
#35B65 #49Q05 #53A10 #58E12 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.04997

Abstract

We prove that if u : B₁ ⊂ ℝ² → ℝⁿ 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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