Paper · Jul 30, 2025

On an area-preserving inverse curvature flow for plane curves

Zezhen Sun, Yuting Wu

math.DGWider flowsarXiv:2507.22366
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Abstract

In this paper, we study a -type area-preserving non-local flow of convex closed plane curves for any . We show that the flow exists globally, the length of evolving curve is non-increasing, and the limiting curve will be a circle in the metric as time .

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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 Two nonlocal inverse curvature flows of convex closed plane curves (Zezhen Sun, 2023)2Sun 2023 On potentials whose level sets are orbits (Philippe Bolle, Marco Mazzucchelli and Andrea Venturelli, 2024)8Bolle 2024 On length-preserving and area-preserving inverse curvature flow of planar curves with singularities (Yunlong Yang, Yanwen Zhao, Jianbo Fang et al., 2024)4Yang 2024 Star-shaped Curves under Gage's Area-preserving Flow and the CSF (Laiyuan Gao, Shicheng Zhang and Yuntao Zhang, 2024)6Gao 2024 On a non-local area-preserving curve flow (Zezhen Sun and Yuting Wu, 2025)1Sun 2025 Inverse curvature flow of closed Legendre curves (Takashi Kagaya and Masatomo Takahashi, 2025)5Kagaya 2025 On length-preserving and area-preserving inverse curvature flows in the hyperbolic plane (Zhishuai Liu and Guoxin Wei, 2026)3Liu 2026 Type-II Singularities of Immersed Locally Convex Curves Evolving under Generalized Anisotropic Gage Area-Preserving Flows with Slow Curvature Speeds (Ze-Yu Ye and Xiao-Liu Wang, 2026)7Ye 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. On a non-local area-preserving curve flow

    Zezhen Sun and Yuting WuWider flows PDF

    Topics Volume-preserving & constrained flows, Other curvature flows · Same authors Zezhen Sun, Yuting Wu · Shared terms “area preserving”, “evolving curves”

  2. Two nonlocal inverse curvature flows of convex closed plane curves

    Zezhen SunWider flows PDF

    Topics Inverse mean curvature flow, Other curvature flows · Same author Zezhen Sun · Shared terms “plane curves”, “closed plane”, “convex closed”

  3. On length-preserving and area-preserving inverse curvature flows in the hyperbolic plane

    Zhishuai Liu and Guoxin WeiWider flows PDF

    Topics Inverse mean curvature flow, Volume-preserving & constrained flows, Other curvature flows · Shared terms “area preserving”, “evolving curves”, “flow exists”

  4. On length-preserving and area-preserving inverse curvature flow of planar curves with singularities

    Yunlong Yang, Yanwen Zhao, Jianbo Fang et al.Wider flows PDF

    Topics Inverse mean curvature flow, Volume-preserving & constrained flows, Other curvature flows · Shared terms “area preserving”

  5. Inverse curvature flow of closed Legendre curves

    Takashi Kagaya and Masatomo TakahashiWider flows PDF

    Topics Inverse mean curvature flow, Other curvature flows

  6. Star-shaped Curves under Gage's Area-preserving Flow and the CSF

    Laiyuan Gao, Shicheng Zhang and Yuntao ZhangWider flows PDF

    Topics Volume-preserving & constrained flows · Shared terms “area preserving”, “evolving curves”, “exists globally”

  7. Type-II Singularities of Immersed Locally Convex Curves Evolving under Generalized Anisotropic Gage Area-Preserving Flows with Slow Curvature Speeds

    Ze-Yu Ye and Xiao-Liu WangWider flows PDF

    Topics Volume-preserving & constrained flows, Other curvature flows · Shared terms “area preserving”, “plane curves”, “closed plane”

  8. On potentials whose level sets are orbits

    Philippe Bolle, Marco Mazzucchelli and Andrea VenturelliWider flows PDF

    Topics Inverse mean curvature flow, Other curvature flows · Shared terms “increasing”

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