PreprintCC BY 4.0arXiv
Negatively Curved Minimal Surfaces in the Round Four-Sphere
Abstract
We construct smooth closed embedded minimal surfaces with everywhere negative Gaussian curvature in the unit round four-sphere. More precisely, for every sufficiently large integer m, our construction gives a minimal surface Σm of genus m2+1 such that Area(Σm)→ 4π2 as m→+∞. This result yields a complete solution to Problem 101 in Yau's 1982 list of open problems.
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BibTeX
@misc{caniato2026negatively,
title = {{Negatively Curved Minimal Surfaces in the Round Four-Sphere}},
author = {Riccardo Caniato},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12238},
eprint = {2610.12238},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12238},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Negatively Curved Minimal Surfaces in the Round Four-Sphere
AU - Riccardo Caniato
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12238
UR - https://arxiv.org/abs/2610.12238
AB - We construct smooth closed embedded minimal surfaces with everywhere negative Gaussian curvature in the unit round four-sphere. More precisely, for every sufficiently large integer m, our construction gives a minimal surface Σ_m of genus m^2+1 such that Area(Σ_m)→ 4π^2 as m→+∞. This result yields a complete solution to Problem 101 in Yau's 1982 list of open problems.
ER -