Paper · Mar 16, 2016

A sharp inscribed radius estimate for fully nonlinear flows

Simon Brendle, Pei-Ken Hung

math.DGWider flowsarXiv:1603.05295v2
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Abstract

We prove a sharp estimate for the inscribed radius under certain fully nonlinear curvature flows. This estimate is asymptotically sharp on cylinders.

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Submitted
Mar 16, 2016
Last revised
Feb 17, 2017 (v2)
Subjects
math.DG

Comments: to appear in Amer J Math

Other curvature flows

Its neighbourhood

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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 Sharp one-sided curvature estimates for fully nonlinear curvature flows and applications to ancient solutions (Mat Langford and Stephen Lynch, 2017)1Langford 2017 Self-similar solutions to fully nonlinear curvature flows by high powers of curvature (Shanze Gao, Haizhong Li and Xianfeng Wang, 2020)7Gao 2020 On a Class of Fully Nonlinear Curvature Flows in Hyperbolic Space (Fang Hong, 2021)8Hong 2021 A class of generalized fully nonlinear curvature flows and its applications (Jinrong Hu, Jiaqian Liu, Di Ma et al., 2022)2Hu 2022 Ancient pancake solutions to fully nonlinear curvature flows (Sathya Rengaswami and Mat Langford, 2023)6Rengaswami 2023 Rotational symmetry of ancient solutions to fully nonlinear curvature flows (A. Cogo, S. Lynch and O. Vičánek Martínez, 2023)5Cogo 2023 Long time behavior of a class of non-homogeneous anisotropic fully nonlinear curvature flows (Weimin Sheng and Jiazhuo Yang, 2025)3Sheng 2025 Local umbilic, convexity and cylindrical estimates for fully nonlinear curvature flows (Mat Langford and James McCoy, 2025)4Langford 2025
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Sharp one-sided curvature estimates for fully nonlinear curvature flows and applications to ancient solutions

    Mat Langford and Stephen LynchWider flows

    Topics Other curvature flows · Shared terms “fully nonlinear”, “inscribed”, “sharp estimate”

  2. A class of generalized fully nonlinear curvature flows and its applications

    Jinrong Hu, Jiaqian Liu, Di Ma et al.Wider flows

    Topics Other curvature flows · Shared terms “fully nonlinear”, “nonlinear curvature”

  3. Long time behavior of a class of non-homogeneous anisotropic fully nonlinear curvature flows

    Weimin Sheng and Jiazhuo YangWider flows

    Topics Other curvature flows · Shared terms “fully nonlinear”, “nonlinear curvature”

  4. Local umbilic, convexity and cylindrical estimates for fully nonlinear curvature flows

    Mat Langford and James McCoyWider flows

    Topics Other curvature flows · Shared terms “fully nonlinear”, “nonlinear curvature”, “asymptotically sharp”

  5. Rotational symmetry of ancient solutions to fully nonlinear curvature flows

    A. Cogo, S. Lynch and O. Vičánek MartínezWider flows

    Topics Other curvature flows · Shared terms “fully nonlinear”, “nonlinear curvature”

  6. Ancient pancake solutions to fully nonlinear curvature flows

    Sathya Rengaswami and Mat LangfordWider flows

    Topics Other curvature flows · Shared terms “fully nonlinear”, “nonlinear curvature”

  7. Self-similar solutions to fully nonlinear curvature flows by high powers of curvature

    Shanze Gao, Haizhong Li and Xianfeng WangWider flows

    Topics Other curvature flows · Shared terms “fully nonlinear”, “nonlinear curvature”

  8. On a Class of Fully Nonlinear Curvature Flows in Hyperbolic Space

    Fang HongWider flows

    Topics Other curvature flows · Shared terms “fully nonlinear”, “nonlinear curvature”

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Background reading

The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.

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)