Regularity theory for 2-dimensional almost minimal currents. II: Branched center manifold

DOI10.1007/s40818-017-0035-7zbMath1412.49082arXiv1508.05509OpenAlexW1872682865MaRDI QIDQ1661412

Luca Spolaor, Camillo De Lellis, Emanuele Nunzio Spadaro

Publication date: 16 August 2018

Published in: Annals of PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.05509

zbMATH Keywords

center manifoldoptimal regularitybranching singularitiesarea-minimizing currents2-dimensional integral currents

Mathematics Subject Classification ID

Geometric measure and integration theory, integral and normal currents in optimization (49Q15) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15)

Related Items (14)

Multiple valued Jacobi fields ⋮ Dirichlet energy-minimizers with analytic boundary ⋮ On the Boundary Behavior of Mass-Minimizing Integral Currents ⋮ Almgren's type regularity for semicalibrated currents ⋮ The regularity theory for the area functional (in geometric measure theory) ⋮ An upper Minkowski dimension estimate for the interior singular set of area minimizing currents ⋮ Regularity theory for 2-dimensional almost minimal currents I: Lipschitz approximation ⋮ Regularity theory for \(2\)-dimensional almost minimal currents. III: Blowup ⋮ Invariant probability measures from pseudoholomorphic curves. I ⋮ Castelnuovo's bound and rigidity in almost complex geometry ⋮ Boundary regularity of mass-minimizing integral currents and a question of Almgren ⋮ An inequality for length and volume in the complex projective plane ⋮ Nonclassical minimizing surfaces with smooth boundary ⋮ Branch points for (almost-)minimizers of two-phase free boundary problems

Cites Work

• Regularity of area minimizing currents. II: Center manifold
• Regularity of area minimizing currents. III: Blow-up
• Regularity of area minimizing currents I: gradient \(L^p\) estimates
• Tangent cones to two-dimensional area-minimizing integral currents are unique
• Uniqueness of tangent cones for semicalibrated integral 2-cycles
• Multiple valued functions and integral currents
• Almost complex structures and calibrated integral cycles in contact 5-manifolds
• The regularity of Special Legendrian Integral Cycles
• 𝑄-valued functions revisited
• Two Dimensional Area Minimizing Integral Currents are Classical Minimal Surfaces
• Regularity theory for 2-dimensional almost minimal currents I: Lipschitz approximation
• The singular set of J-holomorphic maps into projective algebraic varieties
• Uniqueness of Tangent Cones for Two‐Dimensional Almost‐Minimizing Currents
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