Paper · Nov 26, 2021

A Gauss curvature flow related to the Orlicz-Aleksandrov problem

Bin Chen, Peibiao Zhao

math.DGWider flowsarXiv:2111.13281
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Abstract

In this paper we first obtain the existence of smooth solutions to Orlicz-Aleksandrov problem via a Gauss-like curvature flow.

Comments: arXiv admin note: text overlap with arXiv:1712.07774, arXiv:2001.08862, arXiv:2005.02376, arXiv:2012.11367 by other authors

Other curvature flowsGauss curvature flow

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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 An expanding curvature flow and the (p,q)-Christoffel-Minkowski problems (Bin Chen, Jingshi Cui and Peibiao Zhao, 2022)5Chen 2022 The chord Gauss curvature flow and its Lₚ chord Minkowski problem (Jinrong Hu, Yong Huang, Jian Lu et al., 2023)7Hu 2023 An inverse Gauss curvature flow and its application to p-capacitary Orlicz-Minkowski problem (Bin Chen, Weidong Wang, Xia Zhao et al., 2023)1Chen 2023 Flow by Gauss Curvature to the orlicz Chord Minkowski Problem (Xia Zhao and Peibiao Zhao, 2023)3Zhao 2023 Flow by Gauss Curvature to the Orlicz Minkowski Problem for q-torsional rigidity (Xia Zhao and Peibiao Zhao, 2024)2Zhao 2024 Gauss curvature flow to the Lₚ-Gaussian chord Minkowski problem (Xia Zhao and Peibiao Zhao, 2024)4Zhao 2024 Regularity of the p-Gauss curvature flow with flat side (Genggeng Huang, Xu-Jia Wang and Yang Zhou, 2024)8Huang 2024 The dual Minkowski problem for q-torsional rigidity (Xia Zhao and Peibiao Zhao, 2024)6Zhao 2024
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. An inverse Gauss curvature flow and its application to p-capacitary Orlicz-Minkowski problem

    Bin Chen, Weidong Wang, Xia Zhao et al.Wider flows PDF

    Topics Gauss curvature flow, Other curvature flows · Same authors Bin Chen, Peibiao Zhao · Shared terms “Orlicz”, “smooth solutions”

  2. Flow by Gauss Curvature to the Orlicz Minkowski Problem for q-torsional rigidity

    Xia Zhao and Peibiao ZhaoWider flows PDF

    Topics Gauss curvature flow, Other curvature flows · Same author Peibiao Zhao · Shared terms “Orlicz”

  3. Flow by Gauss Curvature to the orlicz Chord Minkowski Problem

    Xia Zhao and Peibiao ZhaoWider flows PDF

    Topics Gauss curvature flow, Other curvature flows · Same author Peibiao Zhao · Shared terms “Orlicz”, “smooth solutions”

  4. Gauss curvature flow to the -Gaussian chord Minkowski problem

    Xia Zhao and Peibiao ZhaoWider flows PDF

    Topics Gauss curvature flow, Other curvature flows · Same author Peibiao Zhao · Shared terms “smooth solutions”

  5. An expanding curvature flow and the (p,q)-Christoffel-Minkowski problems

    Bin Chen, Jingshi Cui and Peibiao ZhaoWider flows PDF

    Topics Gauss curvature flow, Other curvature flows · Same authors Bin Chen, Peibiao Zhao · Shared terms “smooth solutions”

  6. The dual Minkowski problem for -torsional rigidity

    Xia Zhao and Peibiao ZhaoWider flows PDF

    Topics Gauss curvature flow, Other curvature flows · Same author Peibiao Zhao · Shared terms “Orlicz”

  7. The chord Gauss curvature flow and its chord Minkowski problem

    Jinrong Hu, Yong Huang, Jian Lu et al.Wider flows PDF

    Topics Gauss curvature flow, Other curvature flows

  8. Regularity of the -Gauss curvature flow with flat side

    Genggeng Huang, Xu-Jia Wang and Yang ZhouWider flows PDF

    Topics Gauss curvature flow, Other curvature flows

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Background reading

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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) Gauss curvature flow Wider flows Convex hypersurfaces shrink with normal speed a power K^α of their Gauss curvature. Firey proposed it as a model of stones worn by waves; for α>… Start with: Shapes of worn stones (Firey, 1974)