Genus one critical catenoid
Differential Geometry
2024-09-20 v1
Abstract
We use variational methods to construct a free boundary minimal surface in the three-dimensional unit ball with genus one, two boundary components and prismatic symmetry. Key ingredients are an extension of the equivariant min-max theory to include orientation-reversing isometries and the discovery of a nontrivial two-parameter sweepout.
Keywords
Cite
@article{arxiv.2409.12588,
title = {Genus one critical catenoid},
author = {Giada Franz and Daniel Ketover and Mario B. Schulz},
journal= {arXiv preprint arXiv:2409.12588},
year = {2024}
}