Minimal hypertori in the four-dimensional sphere
Differential Geometry
2023-09-26 v3
Abstract
We prove that the four-dimensional round sphere contains a minimally embedded hypertorus, as well as infinitely many, pairwise non-isometric, immersed ones. Our analysis also yields infinitely many, pairwise non-isometric, minimally embedded hyperspheres and thus provides a self-contained solution to Chern's spherical Bernstein conjecture in dimensions four and six.
Cite
@article{arxiv.2109.11768,
title = {Minimal hypertori in the four-dimensional sphere},
author = {Alessandro Carlotto and Mario B. Schulz},
journal= {arXiv preprint arXiv:2109.11768},
year = {2023}
}
Comments
Published version with the journal's style file. 33 pages, 7 figures