PreprintCC BY 4.0arXiv
Regularity for the prescribed vertical mean curvature system in the plane
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 Lr, r > 2. This strengthens and extends our previous result on the Lawson-Osserman conjecture, https://arxiv.org/abs/2308.04997.
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BibTeX
@misc{hirsch2026regularity,
title = {{Regularity for the prescribed vertical mean curvature system in the plane}},
author = {Jonas Hirsch and Connor Mooney and Riccardo Tione},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01970},
eprint = {2610.01970},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01970},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Regularity for the prescribed vertical mean curvature system in the plane
AU - Jonas Hirsch
AU - Connor Mooney
AU - Riccardo Tione
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01970
UR - https://arxiv.org/abs/2610.01970
AB - 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.
ER -