Paper · May 5, 2017

Some remarks on Huisken's monotonicity formula for mean curvature flow

Carlo Mantegazza, Annibale Magni

math.APWider flowsarXiv:1705.02159
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Abstract

We discuss a monotone quantity related to Huisken's monotonicity formula and some technical consequences for mean curvature flow.

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Submitted
May 5, 2017
Subjects
math.AP

Comments: in "Singularities in nonlinear evolution phenomena and applications", 157-169, CRM Series, 9, Ed. Sc. Norm. Pisa, 2009

Mean curvature flow

Its neighbourhood

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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 Volume growth, entropy and stability for translating solitons (Qiang Guang, 2016)4Guang 2016 Lectures on curvature flow of networks (Carlo MAntegazza, Matteo Novaga and Alessandra Pluda, 2019)8MAntegazza 2019 Superconvexity of the Heat Kernel on Hyperbolic Space (Yongzhe Zhang, 2020)3Zhang 2020 The Boundary Term in Huisken's Monotonicity Formula and the Entropy of Translators (Brian White, 2022)1White 2022 Type-0 singularities in the network flow – Evolution of trees (Carlo Mantegazza, Matteo Novaga and Alessandra Pluda, 2022)7Mantegazza 2022 Monotone Quantities for p-Harmonic functions and the Sharp p-Penrose inequality (Liam Mazurowski and Xuan Yao, 2023)6Mazurowski 2023 Fine properties of nonlinear potentials and a unified perspective on monotonicity formulas (Luca Benatti, Alessandra Pluda and Marco Pozzetta, 2024)5Benatti 2024 A note on Huisken monotonicity-type formula for the mean curvature flow in a gradient shrinking extended Ricci soliton background (José N. V. Gomes, Matheus Hudson and Hikaru Yamamoto, 2024)2Gomes 2024
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. The Boundary Term in Huisken's Monotonicity Formula and the Entropy of Translators

    Brian WhiteWider flows

    Topics Mean curvature flow · Shared terms “Huisken monotonicity”, “monotonicity formula”

  2. A note on Huisken monotonicity-type formula for the mean curvature flow in a gradient shrinking extended Ricci soliton background

    José N. V. Gomes, Matheus Hudson and Hikaru Yamamoto

    Topics Mean curvature flow · Shared terms “Huisken monotonicity”

  3. Superconvexity of the Heat Kernel on Hyperbolic Space

    Yongzhe ZhangWider flows

    Topics Mean curvature flow · Shared terms “Huisken monotonicity”, “monotonicity formula”

  4. Volume growth, entropy and stability for translating solitons

    Qiang GuangWider flows

    Topics Mean curvature flow · Shared terms “Huisken monotonicity”, “monotonicity formula”

  5. Fine properties of nonlinear potentials and a unified perspective on monotonicity formulas

    Luca Benatti, Alessandra Pluda and Marco PozzettaWider flows

    Topics Mean curvature flow · Shared terms “monotonicity formula”, “monotone quantities”

  6. Monotone Quantities for -Harmonic functions and the Sharp -Penrose inequality

    Liam Mazurowski and Xuan YaoWider flows

    Topics Mean curvature flow · Shared terms “monotone quantities”, “monotonicity formula”

  7. Type-0 singularities in the network flow – Evolution of trees

    Carlo Mantegazza, Matteo Novaga and Alessandra PludaWider flows

    Topics Mean curvature flow · Same author Carlo Mantegazza

  8. Lectures on curvature flow of networks

    Carlo MAntegazza, Matteo Novaga and Alessandra PludaWider flows

    Same author Carlo Mantegazza

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)

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.