On the stability index of hypersurfaces with constant mean curvature in spheres

DOI10.1090/S0002-9939-07-08886-7zbMath1157.53030MaRDI QIDQ5308138

Oscar M. Perdomo, Luis J. Alías, Aldir Brasil Junior

Publication date: 27 September 2007

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

zbMATH Keywords

constant mean curvaturefirst eigenvaluestability operator\(H(r)\)-torus

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 (15)

A new optimal estimate for the first stability eigenvalue of closed hypersurfaces in Riemannian space forms ⋮ A half-space type property in the Euclidean sphere ⋮ Stability index jump for constant mean curvature hypersurfaces of spheres ⋮ Sharp Reilly-type inequalities for a class of elliptic operators on submanifolds ⋮ On the normal stability of triharmonic hypersurfaces in space forms ⋮ Bifurcation of constant mean curvature tori in Euclidean spheres ⋮ A characterization of quadric constant mean curvature hypersurfaces of spheres ⋮ A new bound on the Morse index of constant mean curvature tori of revolution in \(\mathbb S^3\) ⋮ Unnamed Item ⋮ Sharp eigenvalue estimates of closed $H$-hypersurfaces in locally symmetric spaces ⋮ Stability of capillary hypersurfaces in a Euclidean ball ⋮ A lower bound for 𝐿₂ length of second fundamental form on minimal hypersurfaces ⋮ On the first stability eigenvalue of hypersurfaces in the Euclidean and hyperbolic spaces ⋮ On the second variation of the biharmonic Clifford torus in \(\mathbb{S}^4\) ⋮ Stability and the index of biharmonic hypersurfaces in a Riemannian manifold

Cites Work

• Low index minimal hypersurfaces of spheres
• Stability of hypersurfaces of constant mean curvature in Riemannian manifolds
• Eigenvalue and ``twisted eigenvalue problems, applications to CMC surfaces
• Minimal varieties in Riemannian manifolds
• Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
• Minimal Surfaces with Low Index in the Three-Dimensional Sphere
• A characterization of the Clifford torus
• Unnamed Item
• Unnamed Item

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