Translating solitons of the mean curvature flow in the space \(\mathbb{H}^2\times \mathbb{R}\)

DOI10.1007/s00022-018-0447-xzbMath1401.53045arXiv1803.02783OpenAlexW2963915130MaRDI QIDQ1990607

Antonio Bueno

Publication date: 25 October 2018

Published in: Journal of Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.02783

zbMATH Keywords

manifolds with densitytranslating solitonsproduct space \(\mathbb{H}^2\times \mathbb{R}\)

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (9)

Translating solitons in a Lorentzian setting, submersions and cohomogeneity one actions ⋮ Delaunay surfaces of prescribed mean curvature in \(\mathrm{Nil}_3\) and \(\widetilde{SL_2}(\mathbb{R})\) ⋮ Rotational surfaces with prescribed mean curvature in \(\mathbb{H}^2 \times \mathbb{R}\) ⋮ Bi-Halfspace and Convex Hull Theorems for Translating Solitons ⋮ Maximum principles applied to translating solitons of the mean curvature flow in product spaces ⋮ Uniqueness of the translating bowl in \(\mathbb{H}^2\times \mathbb{R}\) ⋮ A Delaunay-type classification result for prescribed mean curvature surfaces in \(\mathbb{M}^2(\kappa) \times \mathbb{R} \) ⋮ Invariant translators of the Heisenberg group ⋮ Rotational hypersurfaces of prescribed mean curvature

Cites Work

• The strong halfspace theorem for minimal surfaces
• Stability of translating solutions to mean curvature flow
• On the topology of translating solitons of the mean curvature flow
• Simply connected constant mean curvature surfaces in \(\mathbb H^2\times\mathbb R\)
• Global properties of constant mean curvature surfaces in \(\mathbb H^2\times\mathbb R\)
• Translating surfaces of the non-parametric mean curvature flow with prescribed contact angle
• Random walk in random groups.
• Convexity estimates for mean curvature flow and singularities of mean convex surfaces
• Elliptic partial differential equations of second order
• Solvability of minimal graph equation under pointwise pinching condition for sectional curvatures
• On the isoperimetric problem in Euclidean space with density
• Entire downward translating solitons to the mean curvature flow in Minkowski space
• The volume preserving mean curvature flow.
• Elliptic regularization and partial regularity for motion by mean curvature

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