Paper · Jul 18, 2018

Self similar solutions to the inverse mean curvature flow in

Jui-En Chang

math.DGWider flowsarXiv:1807.06834v2
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Abstract

In this paper, we obtain a complete list of all self-similar solutions of inverse mean curvature flow in .

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Submitted
Jul 18, 2018
Last revised
Jul 20, 2018 (v2)
Subjects
math.DG

Comments: 12 pages

Mean curvature flowOther curvature flowsInverse mean curvature flow

Its neighbourhood

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 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 Rotational symmetry of self-expanders to the inverse mean curvature flow with cylindrical ends (Gregory Drugan, Frederick Tsz-Ho Fong and Hojoo Lee, 2016)7Drugan 2016 Inverse mean curvature flow in complex hyperbolic space (Giuseppe Pipoli, 2016)8Pipoli 2016 On the inverse mean curvature flow in warped product manifolds (Thomas Mullins, 2016)6Mullins 2016 Existence of self-similar solution of the inverse mean curvature flow (K. M. Hui, 2018)1Hui 2018 Existence of hypercylinder expanders of the inverse mean curvature flow (K. M. Hui, 2018)3Hui 2018 Inverse Mean Curvature Flow with Singularities (Beomjun Choi and Pei-Ken Hung, 2018)2Choi 2018 Uniqueness Theorems of Self-Conformal Solutions to Inverse Curvature Flows (Nicholas Cheng-Hoong Chin, Frederick Tsz-Ho Fong and Jingbo Wan, 2018)5Chin 2018 Another proof of the existence of homothetic solitons of the inverse mean curvature flow (Shu-Yu Hsu, 2020)4Hsu 2020
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Existence of self-similar solution of the inverse mean curvature flow

    K. M. HuiWider flows

    Topics Inverse mean curvature flow, Other curvature flows

  2. Inverse Mean Curvature Flow with Singularities

    Beomjun Choi and Pei-Ken HungWider flows

    Topics Inverse mean curvature flow, Other curvature flows

  3. Existence of hypercylinder expanders of the inverse mean curvature flow

    K. M. Hui

    Topics Inverse mean curvature flow, Other curvature flows

  4. Another proof of the existence of homothetic solitons of the inverse mean curvature flow

    Shu-Yu HsuWider flows

    Topics Inverse mean curvature flow, Other curvature flows

  5. Uniqueness Theorems of Self-Conformal Solutions to Inverse Curvature Flows

    Nicholas Cheng-Hoong Chin, Frederick Tsz-Ho Fong and Jingbo WanWider flows

    Topics Inverse mean curvature flow, Other curvature flows

  6. On the inverse mean curvature flow in warped product manifolds

    Thomas MullinsWider flows

    Topics Inverse mean curvature flow, Other curvature flows

  7. Rotational symmetry of self-expanders to the inverse mean curvature flow with cylindrical ends

    Gregory Drugan, Frederick Tsz-Ho Fong and Hojoo LeeWider flows

    Topics Inverse mean curvature flow, Other curvature flows

  8. Inverse mean curvature flow in complex hyperbolic space

    Giuseppe PipoliWider flows

    Topics Inverse mean curvature flow, Other curvature flows

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) Other curvature flows Wider flows Flows that move a hypersurface or metric by some other function of curvature: Gauss curvature (worn stones), inverse mean curvature (the Penrose… Start with: Shapes of worn stones (Firey, 1974) Inverse mean curvature flow Wider flows A hypersurface expands with normal speed 1/H, the reciprocal of its mean curvature. Huisken and Ilmanen's weak version keeps the Hawking mass… Start with: Flow of nonconvex hypersurfaces into spheres (Gerhardt, 1990)

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.