Paper · Sep 19, 2022

Global regularity of Skew mean curvature flow for small data in dimensions

Jiaxi Huang, Ze Li, Daniel Tataru

math.APWider flowsarXiv:2209.08941
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Abstract

The skew mean curvature flow is an evolution equation for a dimensional manifold immersed into , and which moves along the binormal direction with a speed proportional to its mean curvature. In this article, we prove small data global regularity in low-regularity Sobolev spaces for the skew mean curvature flow in dimensions . This extends the local well-posedness result in.

Comments: 38 pages

Mean curvature flow

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Connected papers

The 6 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 6 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 Local well-posedness of the Skew mean curvature flow for small data in d≥ 2 dimensions (Jiaxi Huang and Daniel Tataru, 2022)1Huang 2022 Mean curvature flow with generic low-entropy initial data II (Otis Chodosh, Christos Mantoulidis and Felix Schulze, 2023)4Chodosh 2023 Global well-posedness in the critical Besov space of the skew mean curvature flow in ℝ^d: d≥ 5 (Ning-An Lai, Jie Shao, Zexian Zhang et al., 2025)3Lai 2025 Local well-posedness of the skew mean curvature flow for large data (Jiaxi Huang and Daniel Tataru, 2025)2Huang 2025 Well-posedness of mean curvature flow (Yongheng Han, 2026)5Han 2026 Well-posedness for the mean curvature flow on the half-space and on bounded domains (Ke Chen, Ruilin Hu and Quoc-Hung Nguyen, 2026)6Chen 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Local well-posedness of the Skew mean curvature flow for small data in dimensions

    Jiaxi Huang and Daniel TataruWider flows PDF

    Topics Mean curvature flow · Same authors Jiaxi Huang, Daniel Tataru · Shared terms “small data”, “skew mean”, “regularity Sobolev”

  2. Local well-posedness of the skew mean curvature flow for large data

    Jiaxi Huang and Daniel TataruWider flows PDF

    Topics Mean curvature flow · Same authors Jiaxi Huang, Daniel Tataru · Shared terms “skew mean”, “regularity Sobolev”, “posedness”

  3. Global well-posedness in the critical Besov space of the skew mean curvature flow in

    Ning-An Lai, Jie Shao, Zexian Zhang et al.Wider flows PDF

    Topics Mean curvature flow · Shared terms “skew mean”, “small data”, “global regularity”

  4. Mean curvature flow with generic low-entropy initial data II

    Otis Chodosh, Christos Mantoulidis and Felix SchulzeWider flows PDF

    Topics Mean curvature flow

  5. Well-posedness of mean curvature flow

    Yongheng HanWider flows PDF

    Topics Mean curvature flow · Shared terms “posedness”

  6. Well-posedness for the mean curvature flow on the half-space and on bounded domains

    Ke Chen, Ruilin Hu and Quoc-Hung NguyenWider flows PDF

    Topics Mean curvature flow · Shared terms “posedness”

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)

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.