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Existence of monotone Morse flow lines of the expander functional

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arxiv 2404.08541 v1 pith:7R3KRIDF submitted 2024-04-12 math.DG math.AP

Jacob Bernstein , Letian Chen , Lu Wang This is my paper · ORCID
classification math.DGmath.AP
keywords flowexpanderfunctionalmonotonemorseself-expandersingularasymptotically
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Self-expanders of positive genus

    math.DG 2025-07 reject novelty 8.0 of 10

    For a broad class of cones in R^3, complete connected self-expanders of any positive genus exist, providing mean curvature flows in which genus drops but does not reach zero.

  2. Convexity of mean convex asymptotically conical self-expanders to the mean curvature flow

    math.DG 2025-08 accept novelty 7.0 of 10

    Every complete mean convex asymptotically conical self-expander in R^{n+1}, n≥3, with a mean convex and weakly convex asymptotic cone is strictly convex.

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