What question did this study set out to answer?

This research aims to construct a Morse flow line connecting a strictly unstable self-expander to a stable one.

March 6, 2026

Existence of monotone Morse flow lines of the expander functional

Key Points

This research aims to construct a Morse flow line connecting a strictly unstable self-expander to a stable one.
Constructed singular Morse flow line of the expander functional.
Analyzed properties of monotonicity in the flow.
Explored stability and instability within asymptotically conical self-expanders.
Successfully demonstrated the existence of a monotone Morse flow line.
Identified a small singular set within the constructed flow.
Connected strictly unstable and stable self-expanders.

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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Cite This Study

Bernstein et al. (Wed,) studied this question.

synapsesocial.com/papers/69aa710d531e4c4a9ff5b5eb https://doi.org/https://doi.org/10.1090/tran/9610

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