Eternal Forced Mean Curvature Flows II - Existence

TL;DR

This paper proves that under certain conditions, gradient flow lines of the scalar curvature functional can be extended into eternal forced mean curvature flows with large forcing terms.

Contribution

It introduces conditions under which scalar curvature gradient flows can be perturbed into eternal forced mean curvature flows.

Findings

Existence of eternal forced mean curvature flows under non-degeneracy conditions

Perturbation of gradient flow lines into eternal flows with large forcing

Extension of scalar curvature flow lines to eternal flows

Abstract

We show that under suitable non-degeneracy conditions, complete gradient flow lines of the scalar curvature functional of a riemannian manifold perturb into eternal forced mean curvature flows with large forcing term.