Eternal forced mean curvature flows I - A compactness result

TL;DR

This paper establishes a compactness theorem for eternal mean curvature flows with forcing terms in hyperbolic manifolds, facilitating the development of Morse/Floer homology theories for constant mean curvature hypersurfaces.

Contribution

It proves a compactness result modulo broken trajectories for eternal mean curvature flows with forcing in hyperbolic manifolds, advancing geometric analysis methods.

Findings

Compactness modulo broken trajectories established

Applicable to Morse/Floer homology construction for CMC hypersurfaces

Framework for analyzing eternal mean curvature flows in hyperbolic spaces

Abstract

With a view to constructing a Morse/Floer homology theory for CMC hypersurfaces, we prove a compactness result modulo broken trajectories for eternal mean curvature flows with forcing term in compact, hyperbolic manifolds.