On stable constant mean curvature surfaces in $\mathbb S^2\times \mathbb R$ and $\mathbb H^2\times \mathbb R $

DOI10.1090/S0002-9947-10-04826-9zbMath1195.53089MaRDI QIDQ3566698

Rabah Souam

Publication date: 8 June 2010

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

stabilityconstant mean curvature

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Optimization of shapes other than minimal surfaces (49Q10)

Related Items

Constant mean curvature spheres in homogeneous three-spheres ⋮ Constant mean curvature spheres in homogeneous three-manifolds ⋮ Stability of constant mean curvature surfaces in three-dimensional warped product manifolds ⋮ The Riemannian quantitative isoperimetric inequality ⋮ Stability of spacelike surfaces with constant mean curvature in Lorentzian manifolds ⋮ Index estimates for surfaces with constant mean curvature in 3-dimensional manifolds ⋮ Unnamed Item ⋮ On the first stability eigenvalue of constant mean curvature surfaces into homogeneous 3-manifolds ⋮ Surfaces generated by the real and imaginary parts of analytic functions: a-deformations that occur independently or simultaneously ⋮ Unnamed Item ⋮ Long time behavior of a quasilinear hyperbolic system modelling elastic membranes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Hopf differential for constant mean curvature surfaces in \(\mathbb S^2 \times \mathbb R\) and \(\mathbb H^2 \times\mathbb R\)
• Global properties of constant mean curvature surfaces in \(\mathbb H^2\times\mathbb R\)
• Totally umbilic surfaces in homogeneous 3-manifolds
• Stability of hypersurfaces with constant mean curvature
• Stability of hypersurfaces of constant mean curvature in Riemannian manifolds
• A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces
• Eigenfunctions and nodal sets
• On stability of stationary hypersurfaces for the partitioning problem for balls in space forms
• On stability of capillary surfaces in a ball
• Deformation and stability of surfaces with constant mean curvature
• Proof of the double bubble conjecture
• The isoperimetric problem in spherical cylinders
• Schwarz' \(P\) and \(D\) surfaces are stable
• On the uniqueness of isoperimetric solutions and imbedded soap bubbles in non-compact symmetric spaces. I
• Stability for hypersurfaces of constant mean curvature with free boundary
• One-sided complete stable minimal surfaces
• Stable periodic constant mean curvature surfaces and mesoscopic phase separation
• Index one minimal surfaces in flat three space forms

This page was built for publication: On stable constant mean curvature surfaces in $\mathbb S^2\times \mathbb R$ and $\mathbb H^2\times \mathbb R $