Paper · Nov 16, 2020

On the Gluing Construction of Translating Solitons to Lagrangian Mean Curvature Flow

Wei-Bo Su

math.DGWider flowsarXiv:2011.07882v2
View PDF View HTML arXiv page

As on arXiv

Abstract

We construct Lagrangian translating solitons by desingularizing the intersection points between Lagrangian Grim Reaper cylinders with the same phase using special Lagrangian Lawlor necks. The resulting Lagrangian translating solitons could have arbitrarily many ends and non-contractible loops.

View PDF View HTML arXiv page
Submitted
Nov 16, 2020
Last revised
Apr 15, 2021 (v2)
Subjects
math.DG

Comments: 29 pages, 4 figures

Mean curvature flowLagrangian mean curvature flowSelf-shrinkers & translators

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 2016, 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 Local non-collapsing of volume for the Lagrangian mean curvature flow (Knut Smoczyk, 2018)7Smoczyk 2018 f-minimal Lagrangian Submanifolds in Kähler Manifolds with Real Holomorphy Potentials (Wei-Bo Su, 2019)8Su 2019 Infinite-Time Singularities of the Lagrangian Mean Curvature Flow (Wei-Bo Su, Chung-Jun Tsai and Albert Wood, 2024)1Su 2024 Translating Solitons to a Lagrangian mean curvature flow with zero Maslov class (Xiaoli Han, Jiayu Li and Jun Sun, 2024)2Han 2024 Type II Singularities of Lagrangian Mean Curvature Flow with Zero Maslov Class (Xiang Li, Yong Luo and Jun Sun, 2024)6Li 2024 Spectral Analysis for Finite-Time Singularities of Lagrangian Mean Curvature Flow (Maxwell Stolarski and Wei-Bo Su, 2026)3Stolarski 2026 Finite-Time Singularities of Lagrangian Mean Curvature Flow with Quantitatively Precise Dynamics (Maxwell Stolarski and Wei-Bo Su, 2026)5Stolarski 2026 Existence of Lagrangian Mean Curvature Flow Singularities with Bounded Mean Curvature (Maxwell Stolarski and Wei-Bo Su, 2026)4Stolarski 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Infinite-Time Singularities of the Lagrangian Mean Curvature Flow

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

    Topics Lagrangian mean curvature flow · Same author Wei-Bo Su · Shared terms “special Lagrangian”, “Lagrangian Lawlor”, “Lawlor necks”

  2. Translating Solitons to a Lagrangian mean curvature flow with zero Maslov class

    Xiaoli Han, Jiayu Li and Jun SunWider flows

    Topics Lagrangian mean curvature flow, Self-shrinkers & translators · Shared terms “translating solitons”, “Lagrangian translating”

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

    Maxwell Stolarski and Wei-Bo SuWider flows

    Topics Lagrangian mean curvature flow, Self-shrinkers & translators · Same author Wei-Bo Su · Shared terms “special Lagrangian”

  4. Existence of Lagrangian Mean Curvature Flow Singularities with Bounded Mean Curvature

    Maxwell Stolarski and Wei-Bo SuWider flows

    Topics Lagrangian mean curvature flow · Same author Wei-Bo Su

  5. Finite-Time Singularities of Lagrangian Mean Curvature Flow with Quantitatively Precise Dynamics

    Maxwell Stolarski and Wei-Bo SuWider flows

    Topics Lagrangian mean curvature flow · Same author Wei-Bo Su · Shared terms “special Lagrangian”, “arbitrarily”

  6. Type II Singularities of Lagrangian Mean Curvature Flow with Zero Maslov Class

    Xiang Li, Yong Luo and Jun SunWider flows

    Topics Lagrangian mean curvature flow, Self-shrinkers & translators · Shared terms “Lagrangian translating”, “translating solitons”, “arbitrarily”

  7. Local non-collapsing of volume for the Lagrangian mean curvature flow

    Knut SmoczykWider flows

    Topics Lagrangian mean curvature flow, Self-shrinkers & translators · Shared terms “Lagrangian translating”, “translating solitons”

  8. -minimal Lagrangian Submanifolds in Kähler Manifolds with Real Holomorphy Potentials

    Wei-Bo Su

    Topics Lagrangian mean curvature flow, Self-shrinkers & translators · Same author Wei-Bo Su · Shared terms “translating solitons”, “special Lagrangian”

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) Self-shrinkers & translators Wider flows Self-similar solutions of mean curvature flow: shrinkers move by scaling, expanders by scaling outward, translators by sliding. Start with: Asymptotic behavior for singularities of the mean curvature flow (Huisken, 1990)

In the guidebook

  1. 6A.10
    Curve Shortening and the First Geometric FlowsBook 6A · The Heat Equation and Its Relatives

    Shrinking circles, grim reapers, neckpinches and Huisken’s monotonicity, seen in the plane.