Volumes of Vector Fields on Spheres

DOI10.2307/2154338zbMath0771.53023OpenAlexW4239287920MaRDI QIDQ4038443

Sharon L. Pedersen

Publication date: 16 May 1993

Full work available at URL: https://doi.org/10.2307/2154338

zbMATH Keywords

Hopf fibrationHopf vector fieldvolume-minimizing cones

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Variational problems concerning extremal problems in several variables; Yang-Mills functionals (58E15)

Related Items

Volume-minimizing cycles in Grassmann manifolds, Volume-minimizing foliations on spheres, Total bending of vector fields on Riemannian manifolds, Gauss maps of harmonic and minimal great circle fibrations, Vector fields with big and small volume on the \(2\)-sphere, On area-minimizing Pfaffian varieties, Regularity of volume-minimizing flows on 3-manifolds, Left-invariant minimal unit vector fields on the solvable Lie group, Minimally immersed Klein bottles in the unit tangent bundle of the unit 2-sphere arising from area-minimizing unit vector fields on \(\mathbb{S}^2\backslash \{ N,S\}\), ENERGY OF GLOBAL FRAMES, Lipschitz minimality of Hopf fibrations and Hopf vector fields, Unit vector fields on antipodally punctured spheres: big index, big volume, A family of stratified area-minimizing cones, Area-minimizing vector fields on round 2-spheres, A critical radius for unit Hopf vector fields on spheres, Total curvature and volume of foliations on the sphere \(S^{2}\), Stability of unit Hopf vector fields on quotients of spheres, Harmonic vector fields on space forms, Poincaré index and the volume functional of unit vector fields on punctured spheres, Area minimizing unit vector fields on antipodally punctured unit 2-sphere, Lower bounds on volumes of vector fields, Minimal unit vector fields

Cites Work

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• The geometry of the Hopf fibrations
• A sufficient criterion for a cone to be area-minimizing
• Volumes of Flows
• MINIMAL COMPACTA IN RIEMANNIAN MANIFOLDS AND REIFENBERG'S CONJECTURE