Existence of monotone Morse flow lines of the expander functional

2024/04/12 by Jacob Bernstein, Bernstein, Jacob, Letian Chen +3 · 3 citations
Mathematics · Physics and Astronomy · #49Q20 #53E10 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2404.08541

openalex publication_date 2024/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a smooth asymptotically conical self-expander that is strictly unstable we construct a (singular) Morse flow line of the expander functional that connects it to a stable self-expander. This flow is monotone in a suitable sense and has small singular set.

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• Non-uniqueness in Mean Curvature Flow: Non-canonical solutions via the parabolic Allen--Cahn
• Convexity of mean convex asymptotically conical self-expanders to the mean curvature flow
• Self-expanders of positive genus

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