Ancient solutions to free boundary mean curvature flow
Differential Geometry
2026-02-10 v1
Abstract
We establish rigidity results for ancient solutions to the free boundary mean curvature flow in manifolds with convex boundary. In particular, we show that any free boundary minimal hypersurface of Morse index I admits an I-parameter family of ancient solutions that emanate from it. Moreover, among ancient solutions that backward converge exponentially fast to the minimal hypersurface, these exhaust all possibilities. Additionally, we construct a smooth free boundary mean convex foliation around an unstable free boundary minimal hypersurface that enables us to provide a more detailed geometric description of mean-convex ancient solutions that backward converge to that minimal surface.
Keywords
Cite
@article{arxiv.2602.08850,
title = {Ancient solutions to free boundary mean curvature flow},
author = {Theodora Bourni and Giada Franz},
journal= {arXiv preprint arXiv:2602.08850},
year = {2026}
}
Comments
27 pages, 1 figure