A Delaunay-type classification result for prescribed mean curvature surfaces in \(\mathbb{M}^2(\kappa) \times \mathbb{R} \)

DOI10.2140/PJM.2021.313.45zbMath1480.53004arXiv1807.10040OpenAlexW3199697574MaRDI QIDQ2234341

Antonio Bueno

Publication date: 19 October 2021

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

Full work available at URL: https://arxiv.org/abs/1807.10040

zbMATH Keywords

product spaceprescribed mean curvaturerotational surfaceDelaunay-type classificationexistence of spheres

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (4)

Delaunay surfaces of prescribed mean curvature in \(\mathrm{Nil}_3\) and \(\widetilde{SL_2}(\mathbb{R})\) ⋮ Rotational surfaces with prescribed mean curvature in \(\mathbb{H}^2 \times \mathbb{R}\) ⋮ Delaunay surfaces of prescribed mean curvature in Berger spheres ⋮ Surfaces of prescribed linear Weingarten curvature in

Cites Work

• A Hopf differential for constant mean curvature surfaces in \(\mathbb S^2 \times \mathbb R\) and \(\mathbb H^2 \times\mathbb R\)
• Simply connected constant mean curvature surfaces in \(\mathbb H^2\times\mathbb R\)
• Removable singularities for sections of Riemannian submersions of prescribed mean curvature
• Translating solitons in Riemannian products
• On the uniqueness of isoperimetric solutions and imbedded soap bubbles in non-compact symmetric spaces. I
• Convex hypersurfaces of prescribed curvatures
• Translating solitons of the mean curvature flow in the space \(\mathbb{H}^2\times \mathbb{R}\)
• Uniqueness of immersed spheres in three-manifolds
• Rotational hypersurfaces of prescribed mean curvature
• Rotational symmetry of Weingarten spheres in homogeneous three-manifolds
• Constant mean curvature surfaces in metric Lie groups
• Isoperimetric domains in the Riemannian product of a circle with a simply connected space form and applications to free boundary problems
• The global geometry of surfaces with prescribed mean curvature in ℝ³
• Cylindrically bounded constant mean curvature surfaces in $\mathbb {H} ^2\times \mathbb {R}$
• Constant mean curvature surfaces in 𝑀²×𝐑

This page was built for publication: A Delaunay-type classification result for prescribed mean curvature surfaces in \(\mathbb{M}^2(\kappa) \times \mathbb{R} \)