Paper · Mar 30, 2023

A convergence rate of periodic homogenization for forced mean curvature flow of graphs in the laminar setting

Jiwoong Jang

math.APWider flowsarXiv:2303.17113v3Nonlinear Differential Equations and Applications NoDEA, Volume 31, article number 36, (2024)
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Abstract

In this paper, we obtain the rate of convergence in periodic homogenization of forced graphical mean curvature flows in the laminated setting. We also discuss with an example that a faster rate cannot be obtained by utilizing Lipscthiz estimates.

Comments: 14 pages

Mean curvature flowVolume-preserving & constrained flows

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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 Level-set forced mean curvature flow with the Neumann boundary condition (Jiwoong Jang, Dohyun Kwon, Hiroyoshi Mitake et al., 2021)2Jang 2021 Capillary-type boundary value problems of mean curvature flow with force and transport terms on a bounded domain (Jiwoong Jang, 2021)4Jang 2021 Uniqueness of blowups for forced mean curvature flow (Sven Hirsch and Jonathan J. Zhu, 2023)3Hirsch 2023 Asymptotic growth rate of solutions to level-set forced mean curvature flows with evolving spirals (Hiroyoshi Mitake and Hung V. Tran, 2023)5Mitake 2023 Quenching for axisymmetric hypersurfaces under forced mean curvature flows (Hiroyoshi Mitake, Yusuke Oka and Hung Vinh Tran, 2024)1Mitake 2024 Existence of weak solutions to volume-preserving mean curvature flow with obstacles (Jiwoong Jang, 2025)6Jang 2025 Existence of flat flows for volume-preserving mean curvature flow with contact angle (Jiwoong Jang, 2025)7Jang 2025 Asymptotic Dynamics of Forced Curvature Flow in a Planar Strip with Robin Boundary Conditions (Tianhong Pu, Xiaoqian Xin, Lixia Yuan et al., 2026)8Pu 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Quenching for axisymmetric hypersurfaces under forced mean curvature flows

    Hiroyoshi Mitake, Yusuke Oka and Hung Vinh TranWider flows PDF

    Topics Volume-preserving & constrained flows · Shared terms “forced mean”, “periodic”

  2. Level-set forced mean curvature flow with the Neumann boundary condition

    Jiwoong Jang, Dohyun Kwon, Hiroyoshi Mitake et al.Wider flows PDF

    Topics Volume-preserving & constrained flows · Same author Jiwoong Jang · Shared terms “forced mean”

  3. Uniqueness of blowups for forced mean curvature flow

    Sven Hirsch and Jonathan J. ZhuWider flows PDF

    Topics Volume-preserving & constrained flows · Shared terms “forced mean”

  4. Capillary-type boundary value problems of mean curvature flow with force and transport terms on a bounded domain

    Jiwoong JangWider flows PDF

    Topics Volume-preserving & constrained flows · Same author Jiwoong Jang · Shared terms “forced mean”

  5. Asymptotic growth rate of solutions to level-set forced mean curvature flows with evolving spirals

    Hiroyoshi Mitake and Hung V. TranWider flows PDF

    Topics Volume-preserving & constrained flows · Shared terms “forced mean”

  6. Existence of weak solutions to volume-preserving mean curvature flow with obstacles

    Jiwoong JangWider flows PDF

    Topics Volume-preserving & constrained flows · Same author Jiwoong Jang

  7. Existence of flat flows for volume-preserving mean curvature flow with contact angle

    Jiwoong JangWider flows PDF

    Topics Volume-preserving & constrained flows · Same author Jiwoong Jang

  8. Asymptotic Dynamics of Forced Curvature Flow in a Planar Strip with Robin Boundary Conditions

    Tianhong Pu, Xiaoqian Xin, Lixia Yuan et al.Wider flows PDF

    Topics Volume-preserving & constrained flows · Shared terms “forced mean”, “graphical”

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) Volume-preserving & constrained flows Wider flows Curvature flows with a constraint: subtract the average of the mean curvature and the enclosed volume stays fixed while area decreases, so spheres… Start with: On an area-preserving evolution equation for plane curves (Gage, 1986)

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.