As on arXiv
Abstract
Given and , we study immersed oriented surfaces in the Euclidean 3-space whose mean curvature and Gauss curvature satisfy , where is the Gauss map. This theory widely generalize some of paramount importance such as the ones constant mean and Gauss curvature surfaces, linear Weingarten surfaces and self-translating solitons of the mean curvature flow. Under mild assumptions on the prescribed function , we exhibit a classification result for rotational surfaces in the case that the underlying fully nonlinear PDE that governs these surfaces is elliptic or hyperbolic.
Comments: 21 pages, 9 figures
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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.
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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”, “immersed”
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Invariant -translators in the Heisenberg group
Topics Self-shrinkers & translators · Same author Antonio Bueno · Shared terms “oriented surfaces”, “curvature surface”, “constant mean”
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The class of grim reapers in
Topics Self-shrinkers & translators · Same author Antonio Bueno
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Invariant -translators for the Gauss curvature flow in Euclidean space
Topics Self-shrinkers & translators · Shared terms “Gauss curvature”, “Gauss map”, “Euclidean”
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Rigidity of solitons of the Gauss curvature flow in Euclidean space
Topics Self-shrinkers & translators · Shared terms “Gauss curvature”, “constant mean”, “translating solitons”
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Rigidity and Non-existence Results of -Translating Solitons
Topics Self-shrinkers & translators · Shared terms “translating solitons”, “immersed”
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Solitons to Mean Curvature Flow in the hyperbolic 3-space
Topics Self-shrinkers & translators · Shared terms “constant mean”, “translating solitons”, “rotational”
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On the second boundary value problem for mean curvature flow in Minkowski space
Topics Self-shrinkers & translators · Shared terms “translating solitons”, “Gauss”
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In the guidebook
- 6A.10Curve Shortening and the First Geometric Flows
Shrinking circles, grim reapers, neckpinches and Huisken’s monotonicity, seen in the plane.