Minimal surfaces with negative curvature in large dimensional spheres
Differential Geometry
2025-11-14 v3
Abstract
In this note, we answer positively a question of Yau by proving the existence of closed minimal surfaces with negative induced curvature in any sphere of large dimension. The proof follows the strategy of Song, applying it to closed Riemann surfaces with large automorphism groups, and obtaining almost hyperbolic minimal surfaces.
Keywords
Cite
@article{arxiv.2510.18618,
title = {Minimal surfaces with negative curvature in large dimensional spheres},
author = {Michele Ancona and François Labourie and Anna Roig Sanchis and Jérémy Toulisse},
journal= {arXiv preprint arXiv:2510.18618},
year = {2025}
}
Comments
12 pages, V2: order name/first name corrected in the Metadata, V3 a wrong shortcut was corrected