As on arXiv
Abstract
We establish the existence of one-parameter families of helicoidal surfaces of which, under mean curvature flow, simultaneously rotate about a vertical axis and translate vertically.
Comments: 10 pages, 4 figures. arXiv admin note: text overlap with arXiv:2307.14136
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.
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Solitons to Mean Curvature Flow in the hyperbolic 3-space
Topics Self-shrinkers & translators · Same authors Ronaldo F. de Lima, Álvaro K. Ramos, João Paulo dos Santos · Shared terms “parameter family”, “helicoidal”
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Dynamical Stability of Translating Solitons to Mean Curvature Flow in Hyperbolic Space
Topics Self-shrinkers & translators · Same authors Ronaldo F. de Lima, Álvaro K. Ramos
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Translators to Higher Order Mean Curvature Flows in and
Topics Self-shrinkers & translators · Same author Ronaldo F. de Lima
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Hessian estimates for shrinkers, expanders, translators, and rotators of the Lagrangian Mean Curvature Flow
Topics Self-shrinkers & translators
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Uniqueness of the -catenary cylinders by their asymptotic behaviour
Topics Self-shrinkers & translators · Same author João Paulo dos Santos · Shared terms “vertical”
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Translating Annuli for Mean Curvature Flow
Topics Self-shrinkers & translators · Shared terms “vertical”
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Classification of Minimal Surfaces and Solitons to the Mean Curvature Flow in as Translation Surfaces
Topics Self-shrinkers & translators · Same author João Paulo dos Santos
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Invariant -translators in the Heisenberg group
Topics Self-shrinkers & translators · Shared terms “helicoidal”, “vertical”
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.