Paper · May 28, 2018

Graphical Translators for Mean Curvature Flow

David Hoffman, Tom Ilmanen, Francisco Martin, Brian White

math.DGWider flowsarXiv:1805.10860v4
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As on arXiv

Abstract

In this paper we provide a full classification of complete translating graphs in . We also construct two -parameter families of new examples of translating graphs in .

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Submitted
May 28, 2018
Last revised
Nov 18, 2025 (v4)
Subjects
math.DG, math.AP

Comments: In the published version of the article, there was an incorrect reference, and, consequently, a correction appeared in a subsequent issue of the journal. There was no change in the statements or proofs of the results in the article

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 Notes on translating solitons for Mean Curvature Flow (David Hoffman, Tom Ilmanen, Francisco Martín et al., 2019)1Hoffman 2019 Scherk-like Translators for Mean Curvature Flow (David Hoffman, Francisco Martín and Brian White, 2019)5Hoffman 2019 Nguyen's Tridents and the Classification of Semigraphical Translators for Mean Curvature Flow (David Hoffman, Francisco Martín and Brian White, 2019)4Hoffman 2019 Graphical translators for anisotropic and crystalline mean curvature flow (Annalisa Cesaroni, Heiko Kroener and Matteo Novaga, 2021)8Cesaroni 2021 Annuloids and Δ-wings (D. Hoffman, F. Martin and B. White, 2023)2Hoffman 2023 Translating Annuli for Mean Curvature Flow (David Hoffman, Francisco Martín and Brian White, 2023)3Hoffman 2023 Classification of Semigraphical Translators (Francisco Martín, Mariel Sáez, Raphael Tsiamis et al., 2024)6Martín 2024 Dynamical stability of various convex graphical translators (Junyoung Park, 2026)7Park 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Notes on translating solitons for Mean Curvature Flow

    David Hoffman, Tom Ilmanen, Francisco Martín et al.Wider flows

    Topics Self-shrinkers & translators · Same authors David Hoffman, Tom Ilmanen, Francisco Martin · Shared terms “translating graphs”, “complete translating”, “full classification”

  2. Annuloids and -wings

    D. Hoffman, F. Martin and B. WhiteWider flows

    Topics Self-shrinkers & translators · Same authors David Hoffman, Francisco Martin, Brian White · Shared terms “translating graphs”, “complete translating”

  3. Translating Annuli for Mean Curvature Flow

    David Hoffman, Francisco Martín and Brian WhiteWider flows

    Topics Self-shrinkers & translators · Same authors David Hoffman, Francisco Martin, Brian White

  4. Nguyen's Tridents and the Classification of Semigraphical Translators for Mean Curvature Flow

    David Hoffman, Francisco Martín and Brian WhiteWider flows

    Topics Self-shrinkers & translators · Same authors David Hoffman, Francisco Martin, Brian White · Shared terms “parameter family”

  5. Scherk-like Translators for Mean Curvature Flow

    David Hoffman, Francisco Martín and Brian WhiteWider flows

    Topics Self-shrinkers & translators · Same authors David Hoffman, Francisco Martin, Brian White · Shared terms “parameter family”

  6. Classification of Semigraphical Translators

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

    Topics Self-shrinkers & translators · Same authors Francisco Martin, Brian White

  7. Dynamical stability of various convex graphical translators

    Junyoung ParkWider flows

    Topics Self-shrinkers & translators · Shared terms “graphical translators”

  8. Graphical translators for anisotropic and crystalline mean curvature flow

    Annalisa Cesaroni, Heiko Kroener and Matteo NovagaWider flows

    Topics Self-shrinkers & translators · Shared terms “graphical translators”

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.

Foundational paper in the Self-shrinkers & translators guide: Hoffman–Ilmanen–Martín–White: the complete translating graphs in .

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) 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.