Ruled surfaces of generalized self-similar solutions of the mean curvature flow

DOI10.1007/S00009-021-01843-0zbMath1477.53119arXiv2005.07660OpenAlexW3197317813MaRDI QIDQ821501

Rafael López

Publication date: 20 September 2021

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.07660

zbMATH Keywords

mean curvature flowruled surfaceself-similar solutionseparation of variables

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Surfaces in Euclidean and related spaces (53A05) Ricci flows (53E20)

Related Items (3)

Ruled surfaces as translating solitons of the inverse mean curvature flow in the three-dimensional Lorentz-Minkowski space ⋮ Self-similar solutions to the MCF in \(\mathbb{R}^3\) ⋮ Some rigidity properties for \(\lambda\)-self-expanders

Cites Work

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• Rigidity theorems of \(\lambda\)-hypersurfaces
• The hyperplane is the only stable, smooth solution to the isoperimetric problem in Gaussian space
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• Isoperimetry of waists and concentration of maps
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• A survey of closed self-shrinkers with symmetry
• Complete \(\lambda \)-hypersurfaces of weighted volume-preserving mean curvature flow
• Helicoidal surfaces rotating/translating under the mean curvature flow
• On the existence of a closed, embedded, rotational \(\lambda \)-hypersurface
• 1-dimensional solutions of the \(\lambda \)-self shrinkers
• Self-similar solutions to the curve shortening flow
• Gap and rigidity theorems of 𝜆-hypersurfaces
• Self-shrinkers with a rotational symmetry
• Elliptic regularization and partial regularity for motion by mean curvature
• The zoo of solitons for curve shortening in $\mathbb{R}^n$
• Two non existence results for the self-similar equation in Euclidean 3-space

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