On eternal mean curvature flows of tori in perturbations of the unit sphere

Claudia V. S. Magaño and Graham Smith

Vol. 320 (2022), No. 2, 319–363

DOI: 10.2140/pjm.2022.320.319

Abstract

We construct eternal mean curvature flows of tori in perturbations of the standard unit sphere ${\mathbb{𝕊}}^3$. This has applications to the study of the Morse homologies of area functionals over the space of embedded tori in ${\mathbb{𝕊}}^3$.

Keywords

eternal mean curvature flows, singular perturbation, Morse homology

Mathematical Subject Classification

Primary: 53E10

Milestones

Received: 3 June 2020

Revised: 30 November 2021

Accepted: 12 December 2021

Published: 15 February 2023