Paper · Dec 13, 2016

Minimizing movements for mean curvature flow of droplets with prescribed contact angle

Giovanni Bellettini, Shokhrukh Yusufovich Kholmatov

math.APWider flowsarXiv:1612.04175v2
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Abstract

We study the mean curvature motion of a droplet flowing by mean curvature on a horizontal hyperplane with a possibly nonconstant prescribed contact angle. Using the minimizing movements method we show the existence of a weak evolution, and its compatibility with a distributional solution. We also prove various comparison results.

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Submitted
Dec 13, 2016
Last revised
May 16, 2018 (v2)
Subjects
math.AP

Comments: 41 pages, 1 figures

Mean curvature flowWeak & singular flowsFree boundary & capillary

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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 Minimizing movements for mean curvature flow of partitions (Giovanni Bellettini and Shokhrukh Yusufovich Kholmatov, 2017)3Bellettini 2017 Minimizing movements for forced anisotropic mean curvature flow of partitions with mobilities (Giovanni Bellettini, Antonin Chambolle and Shokhrukh Yu. Kholmatov, 2020)6Bellettini 2020 Consistency of minimizing movements with smooth mean curvature flow of droplets with prescribed contact-angle in ℝ³ (Shokhrukh Kholmatov, 2024)1Kholmatov 2024 A convergence result for a minimizing movement scheme for mean curvature flow with prescribed contact angle in a curved domain (Tokuhiro Eto and Yoshikazu Giga, 2024)2Eto 2024 Minimizing movements for forced anisotropic curvature flow of droplets (Shokhrukh Yu. Kholmatov, 2024)8Kholmatov 2024 Minimizing movements for the generalized power mean curvature flow (Giovanni Bellettini and Shokhrukh Yu. Kholmatov, 2024)5Bellettini 2024 Existence of weak mean curvature flow with prescribed contact angle via elliptic regularization (Kiichi Tashiro, 2024)4Tashiro 2024 Convergence of a minimizing movement scheme for contact-angle mean curvature flow in a smooth bounded domain (Tokuhiro Eto and Jiwoong Jang, 2026)7Eto 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Consistency of minimizing movements with smooth mean curvature flow of droplets with prescribed contact-angle in

    Shokhrukh KholmatovWider flows

    Topics Free boundary & capillary, Weak & singular flows · Same author Shokhrukh Yusufovich Kholmatov · Shared terms “prescribed contact”, “contact angle”, “minimizing movements”

  2. A convergence result for a minimizing movement scheme for mean curvature flow with prescribed contact angle in a curved domain

    Tokuhiro Eto and Yoshikazu GigaWider flows

    Topics Free boundary & capillary, Weak & singular flows · Shared terms “prescribed contact”, “contact angle”, “minimizing movements”

  3. Minimizing movements for mean curvature flow of partitions

    Giovanni Bellettini and Shokhrukh Yusufovich KholmatovWider flows

    Topics Weak & singular flows · Same authors Giovanni Bellettini, Shokhrukh Yusufovich Kholmatov · Shared terms “minimizing movements”

  4. Existence of weak mean curvature flow with prescribed contact angle via elliptic regularization

    Kiichi TashiroWider flows

    Topics Free boundary & capillary, Weak & singular flows · Shared terms “prescribed contact”, “contact angle”

  5. Minimizing movements for the generalized power mean curvature flow

    Giovanni Bellettini and Shokhrukh Yu. KholmatovWider flows

    Topics Weak & singular flows · Same authors Giovanni Bellettini, Shokhrukh Yusufovich Kholmatov · Shared terms “minimizing movements”

  6. Minimizing movements for forced anisotropic mean curvature flow of partitions with mobilities

    Giovanni Bellettini, Antonin Chambolle and Shokhrukh Yu. KholmatovWider flows

    Topics Weak & singular flows · Same authors Giovanni Bellettini, Shokhrukh Yusufovich Kholmatov · Shared terms “minimizing movements”

  7. Convergence of a minimizing movement scheme for contact-angle mean curvature flow in a smooth bounded domain

    Tokuhiro Eto and Jiwoong JangWider flows

    Topics Free boundary & capillary, Weak & singular flows · Shared terms “contact angle”, “prescribed contact”, “minimizing movements”

  8. Minimizing movements for forced anisotropic curvature flow of droplets

    Shokhrukh Yu. KholmatovWider flows

    Topics Weak & singular flows · Same author Shokhrukh Yusufovich Kholmatov · Shared terms “minimizing movements”, “horizontal hyperplane”, “comparison”

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) Weak & singular flows Running a flow when the data isn't smooth or singularities form: Ricci flows from rough initial data, through singularities and on metric measure… Start with: Deformation of C⁰ Riemannian metrics in the direction of their Ricci curvature (Simon, 2002) Free boundary & capillary Flows whose boundary is free to slide on a support surface, meeting it at a right angle (free boundary) or at a fixed angle (capillary). Start with: Non-parametric mean curvature evolution with boundary conditions (Huisken, 1989)

In the guidebook

  1. 12C.9
    After PerelmanBook 12C · Extinction and the Proof

    Singular flows, the Smale conjecture, and Bamler’s theory.

  2. 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.