Work

Regularity for the prescribed vertical mean curvature system in the plane

Year: 2026

Type: preprint

Abstract: We prove everywhere regularity for Lipschitz solutions to the prescribed vertical mean curvature system in the plane, where the codimension is arbitrary and the mean curvature is in $L^r, \, r > 2$. This strengthens and extends our previous result on the Lawson-Osserman conjecture, https://arxiv.org/abs/2308.04997.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.01970

Authors: Hirsch, Jonas, Mooney, Connor, Tione, Riccardo

Institutions: Leipzig University, University of California, Irvine, University of Turin

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Ministero dell'Università e della Ricerca

Award: CAREER: Singular and Global Solutions to Nonlinear Elliptic Equations

OpenAlex ID: W7216496871

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