Lower bounds for the index of compact constant mean curvature surfaces in \(\mathbb{R}^3\) and \(\mathbb S^3\)
From MaRDI portal
Publication:2177516
DOI10.4171/rmi/1125zbMath1437.53044arXiv1711.07233OpenAlexW2971515122MaRDI QIDQ2177516
Darlan Ferreira de Oliveira, Marcos Petrúcio De A. Cavalcante
Publication date: 6 May 2020
Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1711.07233
Estimates of eigenvalues in context of PDEs (35P15) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Optimization of shapes other than minimal surfaces (49Q10)
Related Items
Index estimates for closed minimal submanifolds of the sphere, Stability for a second type partitioning problem, On the genus and area of constant mean curvature surfaces with bounded index, Morse index bounds for minimal submanifolds
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Embedded minimal tori in \(S^3\) and the Lawson conjecture
- On the topology and index of minimal surfaces
- A new bound on the Morse index of constant mean curvature tori of revolution in \(\mathbb S^3\)
- Gluing constructions amongst constant mean curvature hypersurfaces in \({\mathbb {S}^{n+1}}\)
- Compact constant mean curvature surfaces in Euclidean three-space
- Index and stability of harmonic Gauss maps
- Constant mean curvature hypersurfaces in \({{\mathbb S}^{n+1}}\) by gluing spherical building blocks
- Complete constant mean curvature surfaces in Euclidean three-space
- All constant mean curvature tori in \(R^ 3\), \(S^ 3\), \(H^ 3\) in terms of theta-functions
- Morse index of constant mean curvature tori of revolution in the 3-sphere
- Stability of hypersurfaces with constant mean curvature
- On complete minimal surfaces with finite Morse index in three manifolds
- Counterexample to a conjecture of H. Hopf
- Stability of hypersurfaces of constant mean curvature in Riemannian manifolds
- Differential geometry in the large. Seminar lectures New York University 1946 and Stanford University 1956. With a preface by S. S. Chern.
- Eigenvalue and ``twisted eigenvalue problems, applications to CMC surfaces
- Index and topology of minimal hypersurfaces in \(\mathbb {R}^n\)
- Comparing the Morse index and the first Betti number of minimal hypersurfaces
- On the classification of constant mean curvature tori
- Constant mean curvature surfaces constructed by fusing Wente tori
- Stability index jump for constant mean curvature hypersurfaces of spheres
- Bifurcation of constant mean curvature tori in Euclidean spheres
- Embedded constant mean curvature tori in the three-sphere
- Generalized doubling constructions for constant mean curvature hypersurfaces in \(S^{ n +1}\)
- One-sided complete stable minimal surfaces
- Minimal varieties in Riemannian manifolds
- Compact stable constant mean curvature surfaces in homogeneous 3-manifolds
- Minimal Surfaces with Low Index in the Three-Dimensional Sphere
- Index bounds for minimal hypersurfaces of the sphere
- LOWER BOUNDS FOR MORSE INDEX OF CONSTANT MEAN CURVATURE TORI
- Constant mean curvature tori in terms of elliptic functions.
- The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
- Stable complete minimal surfaces in 𝑅³ are planes
- A Deformation of Tori with Constant Mean Curvature in ℝ 3 to Those in Other Space Forms
- Minimal surfaces - variational theory and applications
- New applications of Min-max Theory
- Lower bounds for index of Wente tori
