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
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.
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Surfaces of prescribed linear Weingarten curvature in
Topics Self-shrinkers & translators · Same authors Antonio Bueno, Irene Ortiz · Shared terms “prescribed function”, “rotational surfaces”, “constant mean”
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Topics Self-shrinkers & translators · Same author Antonio Bueno · Shared terms “prescribed mean”, “prescribed function”, “constant mean”
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Topics Self-shrinkers & translators · Same author Antonio Bueno · Shared terms “prescribed mean”, “prescribed function”, “translating solitons”
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Invariant -translators in Lorentz-Minkowski space
Topics Self-shrinkers & translators · Same authors Antonio Bueno, Irene Ortiz · Shared terms “rotational”, “translating solitons”
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Invariant -translators in the Heisenberg group
Topics Self-shrinkers & translators · Same author Antonio Bueno · Shared terms “constant mean”, “translating solitons”
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Translating solitons of the mean curvature flow in the space
Topics Self-shrinkers & translators · Same author Antonio Bueno · Shared terms “translating solitons”
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The class of grim reapers in
Topics Self-shrinkers & translators · Same author Antonio Bueno
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Solitons to Mean Curvature Flow in the hyperbolic 3-space
Topics Self-shrinkers & translators · Shared terms “catenoid type”, “constant mean”, “rotational”
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.
In the guidebook
- 6A.10Curve Shortening and the First Geometric Flows
Shrinking circles, grim reapers, neckpinches and Huisken’s monotonicity, seen in the plane.