As on arXiv
Abstract
We study singularities along the Lagrangian mean curvature flow with tangent flows given by multiplicity one special Lagrangian cones that are smooth away from the origin. Some results are: uniqueness of all such tangent flows in dimension two; uniqueness in any dimension when the link of the cone is connected; the existence of nontrivial special Lagrangian blowup limits. We also prove a singular version of Imagi-Joyce-dos Santos's uniqueness result of the Lawlor neck. As an application we prove that in any dimension, singularities that admit a tangent flow given by the union of two transverse planes is modeled on shrinking Lawlor necks at suitable scales.
Comments: 66 pages
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Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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Neck pinches along the Lagrangian mean curvature flow of surfaces
Topics Lagrangian mean curvature flow, Singularities · Same author Gábor Székelyhidi · Shared terms “transverse planes”, “tangent flow”
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Generic neck pinch singularities along 2D Lagrangian mean curvature flow
Topics Lagrangian mean curvature flow, Singularities · Same author Gábor Székelyhidi · Shared terms “singularities along”, “Joyce”
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Ancient solutions and translators of Lagrangian mean curvature flow
Topics Lagrangian mean curvature flow · Same author Gábor Székelyhidi · Shared terms “special Lagrangian”
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Infinite-Time Singularities of the Lagrangian Mean Curvature Flow
Topics Lagrangian mean curvature flow, Singularities · Shared terms “special Lagrangian”, “Lawlor necks”, “singularity formation”
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Lagrangian mean curvature flow of surfaces with mean curvature bound
Topics Lagrangian mean curvature flow, Singularities · Shared terms “tangent flow”
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The mean curvature blows up at nondegenerate neck pinch singularities of Lagrangian mean curvature flow
Topics Lagrangian mean curvature flow, Singularities
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Finite-Time Singularities of Lagrangian Mean Curvature Flow with Quantitatively Precise Dynamics
Topics Lagrangian mean curvature flow, Singularities · Shared terms “special Lagrangian”, “Lagrangian cones”, “tangent flow”
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A Priori Estimates for Singularities of the Lagrangian Mean Curvature Flow with Supercritical Phase
Topics Lagrangian mean curvature flow, Singularities
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The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 6A.13Self-Similar Variables and Monotonicity
Changing variables so that self-similar solutions stand still: convergence to the Gaussian, Giga–Kohn blow-up, Gaussian-weighted monotonicity formulas, frequency functions, and the blow-up logic of Huisken, Struwe and Perelman.
- 6C.8Monotonicity, ε-Regularity and Tangent Cones
Monotonicity formulas for minimal surfaces and harmonic maps, small energy implies smoothness, bubble trees, tangent cones and dimension reduction, with soap films, liquid crystals and pseudolocality.
- 11B.4Blow-Ups, Blow-Downs and Splitting at Infinity
Limits of rescaled manifolds and flows: why blow-up limits are nonnegatively curved, what blow-downs see, and how lines appear at infinity.