English

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.

Keywords

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

R2 v1 2026-06-24T06:17:06.706Z