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arXiv · 2602.08850

Ancient solutions to free boundary mean curvature flow

Theodora Bourni·Giada Franz
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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.

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Theodora Bourni, Giada Franz. 2026-02-09. Ancient solutions to free boundary mean curvature flow. https://arxiv.org/abs/2602.08850

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