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.
On the Lawson-Osserman conjecture
Tione, Riccardo
2026-01-01
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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