Paper · Nov 4, 2026

Existence of Lagrangian Mean Curvature Flow Singularities with Bounded Mean Curvature

Maxwell Stolarski, Wei-Bo Su

math.DGWider flowsarXiv:2611.06248
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Abstract

In every dimension , we show there exist Lagrangian mean curvature flows that develop neck pinch singularities such that the mean curvature remains uniformly bounded. This follows from a related result that, under a structural assumption on the singularity formation, the mean curvature at small scales near the singularity can be bounded by the Lagrangian angle at outer scales with suitable weights. Applying this result to a subset of the finite-time Lagrangian mean curvature flow singularities constructed in the companion paper [arXiv:2607.03152] and the infinite-time Lagrangian mean curvature flow singularities constructed by Tsai, Wood, and the second-named author [arXiv:2401.02228] then gives examples of both finite-time and infinite-time singularity formation with uniformly bounded mean curvature.

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Submitted
Nov 4, 2026
Subjects
math.DG, math.AP

Comments: 27 pages, comments welcome

Mean curvature flowLagrangian mean curvature flowSingularities

Its neighbourhood

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.

Connected papers This paper in the centre and the 8 papers closest to it around it, in date order clockwise from the top. The closer a paper sits to the centre, the stronger the connection. This paper Infinite-Time Singularities of the Lagrangian Mean Curvature Flow (Wei-Bo Su, Chung-Jun Tsai and Albert Wood, 2024)3Su 2024 Singularity formations in Lagrangian mean curvature flow (Yang Li and Gábor Székelyhidi, 2024)5Li 2024 Lagrangian mean curvature flow of surfaces with mean curvature bound (Sourav Ghosh, 2025)6Ghosh 2025 Generic neck pinch singularities along 2D Lagrangian mean curvature flow (Gábor Székelyhidi, 2026)8Székelyhidi 2026 Spectral Analysis for Finite-Time Singularities of Lagrangian Mean Curvature Flow (Maxwell Stolarski and Wei-Bo Su, 2026)2Stolarski 2026 Infinite-Time Singularities with Vanishing Mean Curvature for Lagrangian Mean Curvature Flow in Gibbons–Hawking Spaces (Ping-Hung Lee and Chung-Jun Tsai, 2026)7Lee 2026 Finite-Time Singularities of Lagrangian Mean Curvature Flow with Quantitatively Precise Dynamics (Maxwell Stolarski and Wei-Bo Su, 2026)1Stolarski 2026 The mean curvature blows up at nondegenerate neck pinch singularities of Lagrangian mean curvature flow (Jason D. Lotay and Goncalo Oliveira, 2026)4Lotay 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Finite-Time Singularities of Lagrangian Mean Curvature Flow with Quantitatively Precise Dynamics

    Maxwell Stolarski and Wei-Bo SuWider flows

    Topics Lagrangian mean curvature flow, Singularities, Mean curvature flow · Same authors Maxwell Stolarski, Wei-Bo Su · Shared terms “finite time”, “time singularity”, “companion”

  2. Spectral Analysis for Finite-Time Singularities of Lagrangian Mean Curvature Flow

    Maxwell Stolarski and Wei-Bo SuWider flows

    Topics Lagrangian mean curvature flow, Singularities, Mean curvature flow · Same authors Maxwell Stolarski, Wei-Bo Su · Shared terms “finite time”, “time singularity”, “companion”

  3. Infinite-Time Singularities of the Lagrangian Mean Curvature Flow

    Wei-Bo Su, Chung-Jun Tsai and Albert Wood

    Topics Lagrangian mean curvature flow, Singularities, Mean curvature flow · Same author Wei-Bo Su · Shared terms “infinite time”, “time singularity”, “singularity formation”

  4. The mean curvature blows up at nondegenerate neck pinch singularities of Lagrangian mean curvature flow

    Jason D. Lotay and Goncalo OliveiraWider flows

    Topics Lagrangian mean curvature flow, Singularities, Mean curvature flow · Shared terms “neck pinch”, “pinch singularity”

  5. Singularity formations in Lagrangian mean curvature flow

    Yang Li and Gábor SzékelyhidiWider flows

    Topics Lagrangian mean curvature flow, Singularities, Mean curvature flow · Shared terms “singularity formation”

  6. Lagrangian mean curvature flow of surfaces with mean curvature bound

    Sourav GhoshWider flows

    Topics Lagrangian mean curvature flow, Singularities, Mean curvature flow · Shared terms “uniformly bounded”

  7. Infinite-Time Singularities with Vanishing Mean Curvature for Lagrangian Mean Curvature Flow in Gibbons–Hawking Spaces

    Ping-Hung Lee and Chung-Jun TsaiWider flows

    Topics Lagrangian mean curvature flow, Singularities, Mean curvature flow · Shared terms “infinite time”, “time singularity”

  8. Generic neck pinch singularities along 2D Lagrangian mean curvature flow

    Gábor SzékelyhidiWider flows

    Topics Lagrangian mean curvature flow, Singularities, Mean curvature flow · Shared terms “neck pinch”, “pinch singularity”

Read around it

Background reading

The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.

Mean curvature flow Wider flows A hypersurface moves in the direction of its mean curvature vector, which decreases area as fast as possible in the L² sense. Start with: Flow by mean curvature of convex surfaces into spheres (Huisken, 1984) Lagrangian mean curvature flow Wider flows In a Calabi–Yau manifold, mean curvature flow keeps Lagrangian submanifolds Lagrangian. Its hoped-for limits are special Lagrangians, the volume… Start with: A canonical way to deform a Lagrangian submanifold (Smoczyk, 1996) Singularities On a closed manifold the flow can stop in finite time: curvature blows up, often because a neck pinches off. Start with: The formations of singularities in the Ricci Flow (Hamilton, 1993)

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