PreprintCC BY 4.0arXiv
Prescribed mean curvature surfaces of Riemann minimal type
Abstract
We construct analogues of Riemann minimal examples among surfaces in the Euclidean 3-space whose mean curvature is given by a prescribed function on the unit sphere in terms of their Gauss map. Specifically, we obtain a 2-parameter family of complete, properly embedded surfaces foliated by circles and straight lines and invariant under a nontrivial translation.
Related
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- Hypersurfaces of constant higher order mean curvature in hyperbolic space with prescribed asymptotic boundary at infinity
- Existence of disks with prescribed mean curvature and contact angle in arbitrary codimension
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BibTeX
@misc{bueno2026prescribed,
title = {{Prescribed mean curvature surfaces of Riemann minimal type}},
author = {Antonio Bueno},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38563},
eprint = {2610.38563},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38563},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Prescribed mean curvature surfaces of Riemann minimal type
AU - Antonio Bueno
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38563
UR - https://arxiv.org/abs/2610.38563
AB - We construct analogues of Riemann minimal examples among surfaces in the Euclidean 3-space whose mean curvature is given by a prescribed function on the unit sphere in terms of their Gauss map. Specifically, we obtain a 2-parameter family of complete, properly embedded surfaces foliated by circles and straight lines and invariant under a nontrivial translation.
ER -