Area-minimizing vector fields on round 2-spheres

DOI10.1515/CRELLE.2010.020zbMath1187.53029OpenAlexW1979568685MaRDI QIDQ3553931

Olga Gil-Medrano, Vincent Borrelli

Publication date: 22 April 2010

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/crelle.2010.020

zbMATH Keywords

natural metricunit vector fieldsPontryagin cyclePontryagin fieldstangent bundle \(TS^{n}\)

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15)

Related Items

Vector fields with big and small volume on the \(2\)-sphere ⋮ Area minimizing projective planes on the projective space of dimension 3 with the Berger metric ⋮ Minimally immersed Klein bottles in the unit tangent bundle of the unit 2-sphere arising from area-minimizing unit vector fields on \(\mathbb{S}^2\backslash \{ N,S\}\) ⋮ Calibrations for the volume of unit vector fields in dimension 2 ⋮ Unnamed Item ⋮ Poincaré index and the volume functional of unit vector fields on punctured spheres ⋮ Area minimizing unit vector fields on antipodally punctured unit 2-sphere

Cites Work

• On the volume of a unit vector field on the three-sphere
• On the tangent sphere bundle of a 2-sphere
• Minimal unit vector fields
• Energy and volume of unit vector fields on three-dimensional Riemannian manifolds.
• On the volume of unit vector fields on spaces of constant sectional curvature
• A critical radius for unit Hopf vector fields on spheres
• Partial regularity of mass-minimizing rectifiable sections
• Volumes of Vector Fields on Spheres
• Volumes of Flows
• MINIMAL COMPACTA IN RIEMANNIAN MANIFOLDS AND REIFENBERG'S CONJECTURE
• The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension
• Volume, energy and generalized energy of unit vector fields on Berger spheres: stability of Hopf vector fields
• Boundary regularity and embedded solutions for the oriented Plateau problem

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