Comparison between second variation of area and second variation of energy of a minimal surface

DOI10.1515/ACV.2008.009zbMath1163.58006arXiv0708.2188OpenAlexW1973924969WikidataQ125909122 ScholiaQ125909122MaRDI QIDQ3546158

Mario J. Micallef, Norio Ejiri

Publication date: 18 December 2008

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0708.2188

zbMATH Keywords

minimal surfaceMorse indexharmonic map

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12)

Related Items (16)

On stability of the fibres of Hopf surfaces as harmonic maps and minimal surfaces ⋮ Jacobi fields along harmonic 2-spheres in 3- and 4-spheres are not all integrable ⋮ Minimal hypersurfaces with bounded index ⋮ On the space of \(f\)-minimal surfaces with bounded \(f\)-index in weighted smooth metric spaces ⋮ Existence of constant mean curvature 2‐Spheres in Riemannian 3‐spheres ⋮ Smooth compactness of 𝑓-minimal hypersurfaces with bounded 𝑓-index ⋮ Inequivalent complexity criteria for free boundary minimal surfaces ⋮ On the topology and index of minimal surfaces. II ⋮ Morse index, Betti numbers, and singular set of bounded area minimal hypersurfaces ⋮ Existence of harmonic maps and eigenvalue optimization in higher dimensions ⋮ Qualitative and quantitative estimates for minimal hypersurfaces with bounded index and area ⋮ A proof of the multiplicity 1 conjecture for min-max minimal surfaces in arbitrary codimension ⋮ Morse index bound for minimal two spheres ⋮ Bubbling analysis and geometric convergence results for free boundary minimal surfaces ⋮ The second variation for null-torsion holomorphic curves in the 6-sphere ⋮ Sharp eigenvalue bounds and minimal surfaces in the ball

Cites Work

• Index and flat ends of minimal surfaces
• Index, vision number and stability of complete minimal surfaces
• On complete minimal surfaces with finite Morse index in three manifolds
• Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature
• The existence of minimal immersions of 2-spheres
• Morse index and Gauss maps of complete minimal surfaces in Euclidean 3- space
• Schrödinger operators and index bounds for minimal submanifolds
• Compact minimal hypersurfaces with index one in the real projective space
• Complete minimal surfaces with index one and stable constant mean curvature surfaces
• Minimal surfaces of higher topological structure
• The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
• Isoperimetric properties of higher eigenvalues of elliptic operators
• Homotopically energy-minimizing harmonic maps of tori into \(\mathbb{R} P^3\)

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