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Abstract
A -translator is a surface in Euclidean space \r^3 that moves by translations in a spatial direction and under the -flow, where is the Gauss curvature and is a constant. We classify all -translators that are rotationally symmetric. In particular, we prove that for each there is a -translator intersecting orthogonally the rotation axis. We also describe all -translators invariant by a uniparametric group of helicoidal motions and the translators obtained by separation of variables.
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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 for the Gauss curvature flow in Euclidean space
Topics Gauss curvature flow, Self-shrinkers & translators, Other curvature flows · Same authors Muhittin Evren Aydin, Rafael López · Shared terms “Euclidean space”, “rotations”, “translations”
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Classification of invariant Gauss curvature solitons in the Heisenberg space
Topics Gauss curvature flow, Other curvature flows · Same author Rafael López · Shared terms “helicoidal motions”, “translations”
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-translators of offset surfaces
Topics Gauss curvature flow, Rotational symmetry & warped products, Self-shrinkers & translators · Shared terms “Euclidean space”, “direction”
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Rigidity of solitons of the Gauss curvature flow in Euclidean space
Topics Gauss curvature flow, Self-shrinkers & translators, Other curvature flows · Same author Rafael López · Shared terms “Euclidean space”
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Gauss curvature solitons on invariant surfaces in the homogeneous space Sol
Topics Gauss curvature flow, Other curvature flows · Same author Rafael López · Shared terms “translations”
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The class of grim reapers in
Topics Self-shrinkers & translators · Same author Rafael López · Shared terms “translators invariant”, “translations”
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Gauss Curvature Flow on Surfaces of Revolution – The Noncompact Case
Topics Gauss curvature flow, Rotational symmetry & warped products, Other curvature flows
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Invariant -translators in the Heisenberg group
Topics Self-shrinkers & translators · Shared terms “helicoidal motions”, “translators invariant”, “rotations”
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