Paper · Jan 5, 2024

Gauss Curvature Flow on Surfaces of Revolution – The Noncompact Case

Thalia D. Jeffres, Leonardo Solanilla

math.DGWider flowsarXiv:2401.02768
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Abstract

Earlier work of the first author examined two boundary value problems associated to the Gauss Curvature Flow on a surface of revolution generated by a positive, differentiable function on a compact interval. In this continuation, two noncompact cases are addressed.

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Submitted
Jan 5, 2024
Subjects
math.DG
Other curvature flowsGauss curvature flowSurfacesBoundaries & non-compactRotational symmetry & warped products

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 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 A Gauss curvature flow related to the Orlicz-Aleksandrov problem (Bin Chen and Peibiao Zhao, 2021)7Chen 2021 Translators of the Gauss curvature flow (Muhittin Evren Aydin and Rafael López, 2022)2Aydin 2022 Rotational Solitons for the Curve Shortening Flow on Revolution Surfaces (Hiuri dos Reis, Benedito Leandro and Rafael Novais, 2022)3dos Reis 2022 The chord Gauss curvature flow and its Lₚ chord Minkowski problem (Jinrong Hu, Yong Huang, Jian Lu et al., 2023)6Hu 2023 Anisotropic Gauss curvature flow of complete non-compact graphs (Shujing Pan and Yong Wei, 2024)8Pan 2024 Regularity of the p-Gauss curvature flow with flat side (Genggeng Huang, Xu-Jia Wang and Yang Zhou, 2024)4Huang 2024 K^α-translators of offset surfaces (Burcu Bektaş Demirci, Ferdağ Kahraman Aksoyak and Murat Babaarslan, 2024)1Demirci 2024 Invariant λ-translators for the Gauss curvature flow in Euclidean space (Muhittin Evren Aydin and Rafael López, 2025)5Aydin 2025
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. -translators of offset surfaces

    Burcu Bektaş Demirci, Ferdağ Kahraman Aksoyak and Murat BabaarslanWider flows

    Topics Gauss curvature flow, Rotational symmetry & warped products, Other curvature flows · Shared terms “revolution”

  2. Translators of the Gauss curvature flow

    Muhittin Evren Aydin and Rafael LópezWider flows

    Topics Gauss curvature flow, Rotational symmetry & warped products, Other curvature flows

  3. Rotational Solitons for the Curve Shortening Flow on Revolution Surfaces

    Hiuri dos Reis, Benedito Leandro and Rafael NovaisWider flows

    Topics Surfaces · Shared terms “revolution”

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

    Genggeng Huang, Xu-Jia Wang and Yang ZhouWider flows

    Topics Gauss curvature flow, Other curvature flows

  5. Invariant -translators for the Gauss curvature flow in Euclidean space

    Muhittin Evren Aydin and Rafael LópezWider flows

    Topics Gauss curvature flow, Other curvature flows

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

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

    Topics Gauss curvature flow, Other curvature flows

  7. A Gauss curvature flow related to the Orlicz-Aleksandrov problem

    Bin Chen and Peibiao ZhaoWider flows

    Topics Gauss curvature flow, Other curvature flows

  8. Anisotropic Gauss curvature flow of complete non-compact graphs

    Shujing Pan and Yong WeiWider flows

    Topics Gauss curvature flow, Boundaries & non-compact, 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.

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) Surfaces On surfaces Ricci flow is conformal and scalar. It gives a heat-flow proof of the uniformization theorem: every closed surface converges to constant… Start with: The Ricci flow on surfaces (Hamilton, 1988) Boundaries & non-compact Ricci flow beyond closed manifolds: complete non-compact spaces, manifolds with boundary, and asymptotically flat or hyperbolic ends. Start with: Deforming the metric on complete Riemannian manifolds (Shi, 1989)

In the guidebook

  1. 5A.5
    Uniformization and the Two-Dimensional Ricci FlowBook 5A · Complex Analysis and Conformal Geometry

    Constant-curvature metrics on surfaces, and Ricci flow as a heat equation for the conformal factor.

  2. 11A.12
    Ricci Flow on SurfacesBook 11A · The Ricci Flow: Existence and Maximum Principles

    Uniformization by Ricci flow, and Hamilton’s entropy.