Paper · Apr 22, 2023

Annuloids and -wings

D. Hoffman, F. Martin, B. White

math.DGWider flowsarXiv:2304.11447v2
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Abstract

In this paper, we describe new annular examples of complete translating solitons for the mean curvature flow and how they are related to a family of translating graphs, the -wings. In addition, we will prove several related results that answer questions that arise naturally in this investigation. These results apply to translators in general, not just to graphs or annuli.

Comments: Final version. To appear in Advanced Nonlinear Studies

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 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 The Boundary Term in Huisken's Monotonicity Formula and the Entropy of Translators (Brian White, 2022)4White 2022 Finite entropy translating solitons in slabs (Eddygledson Souza Gama, Francisco Martín and Niels Martin Møller, 2022)3Gama 2022 Translating Annuli for Mean Curvature Flow (David Hoffman, Francisco Martín and Brian White, 2023)1Hoffman 2023 Uniqueness of Semigraphical Translators (Francisco Martín, Mariel Sáez and Raphael Tsiamis, 2023)6Martín 2023 Classification of Semigraphical Translators (Francisco Martín, Mariel Sáez, Raphael Tsiamis et al., 2024)2Martín 2024 Generating Shrinkers by Mean Curvature Flow (David Hoffman, Francisco Martin and Brian White, 2025)8Hoffman 2025 Uniqueness of tangent planes and (non-)removable singularities at infinity for collapsed translators (Eddygledson Souza Gama, Francisco Martín and Niels Martin Møller, 2025)5Gama 2025 Half-space theorems for translating solitons of the r-mean curvature flow (Hilário Alencar, G. Pacelli Bessa and Gregório Silva Neto, 2026)7Alencar 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Translating Annuli for Mean Curvature Flow

    David Hoffman, Francisco Martín and Brian WhiteWider flows PDF

    Topics Self-shrinkers & translators · Same authors D. Hoffman, F. Martin, B. White

  2. Classification of Semigraphical Translators

    Francisco Martín, Mariel Sáez, Raphael Tsiamis et al.Wider flows PDF

    Topics Self-shrinkers & translators · Same authors F. Martin, B. White

  3. Finite entropy translating solitons in slabs

    Eddygledson Souza Gama, Francisco Martín and Niels Martin MøllerWider flows PDF

    Topics Self-shrinkers & translators · Same author F. Martin · Shared terms “translating solitons”

  4. The Boundary Term in Huisken's Monotonicity Formula and the Entropy of Translators

    Brian WhiteWider flows PDF

    Topics Self-shrinkers & translators · Same author B. White

  5. Uniqueness of tangent planes and (non-)removable singularities at infinity for collapsed translators

    Eddygledson Souza Gama, Francisco Martín and Niels Martin MøllerWider flows PDF

    Topics Self-shrinkers & translators · Same author F. Martin · Shared terms “translating solitons”

  6. Uniqueness of Semigraphical Translators

    Francisco Martín, Mariel Sáez and Raphael TsiamisWider flows PDF

    Topics Self-shrinkers & translators · Same author F. Martin

  7. Half-space theorems for translating solitons of the r-mean curvature flow

    Hilário Alencar, G. Pacelli Bessa and Gregório Silva NetoWider flows PDF

    Topics Self-shrinkers & translators · Shared terms “translating solitons”, “complete translating”

  8. Generating Shrinkers by Mean Curvature Flow

    David Hoffman, Francisco Martin and Brian White PDF

    Topics Mean curvature flow · Same authors D. Hoffman, F. Martin, B. White

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. Start with: Flow by mean curvature of convex surfaces into spheres (Huisken, 1984) 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.