Paper · Dec 7, 2020

Surfaces with prescribed mean curvature in

Antonio Bueno, Irene Ortiz

math.DGWider flowsarXiv:2012.03795

As on arXiv

Abstract

In this paper we study rotational surfaces in the space whose mean curvature is given as a prescribed function of their angle function. These surfaces generalize, among others, the ones of constant mean curvature and the translating solitons of the mean curvature flow. Using a phase plane analysis we construct entire rotational graphs, catenoid-type surfaces, and exhibit a classification result when the prescribed function is linear.

Submitted
Dec 7, 2020
Subjects
math.DG

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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 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 The global geometry of surfaces with prescribed mean curvature in ℝ³ (Antonio Bueno, Jose A. Galvez and Pablo Mira, 2018)2Bueno 2018 Translating solitons of the mean curvature flow in the space ℍ²×ℝ (Antonio Bueno, 2018)6Bueno 2018 The Björling problem for prescribed mean curvature surfaces in ℝ³ (Antonio Bueno, 2018)3Bueno 2018 Surfaces of prescribed linear Weingarten curvature in ℝ³ (Antonio Bueno and Irene Ortiz, 2022)1Bueno 2022 Solitons to Mean Curvature Flow in the hyperbolic 3-space (R. F. de Lima, A. K. Ramos and J. P. dos Santos, 2023)8de Lima 2023 The class of grim reapers in ℍ²×ℝ (Antonio Bueno and Rafael López, 2024)7Bueno 2024 Invariant λ-translators in Lorentz-Minkowski space (Antonio Bueno and Irene Ortiz, 2024)4Bueno 2024 Invariant λ-translators in the Heisenberg group (Antonio Bueno, 2026)5Bueno 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Surfaces of prescribed linear Weingarten curvature in

    Antonio Bueno and Irene OrtizWider flows

    Topics Self-shrinkers & translators · Same authors Antonio Bueno, Irene Ortiz · Shared terms “prescribed function”, “rotational surfaces”, “constant mean”

  2. The global geometry of surfaces with prescribed mean curvature in

    Antonio Bueno, Jose A. Galvez and Pablo MiraWider flows

    Topics Self-shrinkers & translators · Same author Antonio Bueno · Shared terms “prescribed mean”, “prescribed function”, “constant mean”

  3. The Björling problem for prescribed mean curvature surfaces in

    Antonio BuenoWider flows

    Topics Self-shrinkers & translators · Same author Antonio Bueno · Shared terms “prescribed mean”, “prescribed function”, “translating solitons”

  4. Invariant -translators in Lorentz-Minkowski space

    Antonio Bueno and Irene OrtizWider flows

    Topics Self-shrinkers & translators · Same authors Antonio Bueno, Irene Ortiz · Shared terms “rotational”, “translating solitons”

  5. Invariant -translators in the Heisenberg group

    Antonio BuenoWider flows

    Topics Self-shrinkers & translators · Same author Antonio Bueno · Shared terms “constant mean”, “translating solitons”

  6. Translating solitons of the mean curvature flow in the space

    Antonio BuenoWider flows

    Topics Self-shrinkers & translators · Same author Antonio Bueno · Shared terms “translating solitons”

  7. The class of grim reapers in

    Antonio Bueno and Rafael LópezWider flows

    Topics Self-shrinkers & translators · Same author Antonio Bueno

  8. Solitons to Mean Curvature Flow in the hyperbolic 3-space

    R. F. de Lima, A. K. Ramos and J. P. dos SantosWider flows

    Topics Self-shrinkers & translators · Shared terms “catenoid type”, “constant mean”, “rotational”

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Background reading

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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.