Regularity of area minimizing currents I: gradient \(L^p\) estimates

DOI10.1007/s00039-014-0306-3zbMath1307.49043arXiv1306.1195OpenAlexW2024165047MaRDI QIDQ484469

Camillo De Lellis, Emanuele Nunzio Spadaro

Publication date: 7 January 2015

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.1195

zbMATH Keywords

Almgren's partial regularityharmonic approximationsLipschitz approximationminimizing currents

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Regularity of solutions in optimal control (49N60) Geometric measure and integration theory, integral and normal currents in optimization (49Q15)

Related Items (29)

Regularity of area minimizing currents. II: Center manifold ⋮ Regularity of area minimizing currents. III: Blow-up ⋮ A variational characterization of complex submanifolds ⋮ Regularity theory for 2-dimensional almost minimal currents. II: Branched center manifold ⋮ Decay rates for the quadratic and super-quadratic tilt-excess of integral varifolds ⋮ On the number of singular points for planar multivalued harmonic functions ⋮ Higher integrability of the gradient for minimizers of the \(2d\) Mumford-Shah energy ⋮ Multiple valued Jacobi fields ⋮ Boundary regularity of minimal oriented hypersurfaces on a manifold ⋮ On the Boundary Behavior of Mass-Minimizing Integral Currents ⋮ Almgren's type regularity for semicalibrated currents ⋮ Partial regularity for mass-minimizing currents in Hilbert spaces ⋮ The regularity theory for the area functional (in geometric measure theory) ⋮ A multiple-valued plateau problem ⋮ The structure of stable codimension one integral varifolds near classical cones of density \(Q+1/2\) ⋮ 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 ⋮ Generic uniqueness for the Plateau problem ⋮ Regularity theory for \(2\)-dimensional almost minimal currents. III: Blowup ⋮ Regularity of area minimizing currents mod \(p\) ⋮ Regularity of area minimizing currents I: gradient \(L^p\) estimates ⋮ The Variations of Yang–Mills Lagrangian ⋮ Convexity at infinity in Cartan-Hadamard manifolds and applications to the asymptotic Dirichlet and Plateau problems ⋮ Rectifiability and upper Minkowski bounds for singularities of harmonic \(Q\)-valued maps ⋮ Boundary regularity of mass-minimizing integral currents and a question of Almgren ⋮ Optimal isoperimetric inequalities for surfaces in any codimension in Cartan-Hadamard manifolds ⋮ Partial Hölder continuity forQ-valued energy minimizing maps ⋮ Higher rank hyperbolicity ⋮ Two-dimensional almost area minimizing currents

Cites Work

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• 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
• Center manifold: A case study
• Uniqueness of tangent cones for semicalibrated integral 2-cycles
• Complex varieties and higher integrability of Dir-minimizing \(Q\)-valued functions
• Approximating \(J\)-holomorphic curves by holomorphic ones
• The singular set of 1-1 integral currents
• On the first variation of a varifold
• Multiple valued functions and integral currents
• The regularity of Special Legendrian Integral Cycles
• Nondoubling weights
• 𝑄-valued functions revisited
• Two Dimensional Area Minimizing Integral Currents are Classical Minimal Surfaces
• Stratification of minimal surfaces, mean curvature flows, and harmonic maps.
• Functions of bounded higher variation
• A lower-epiperimetric inequality for area-minimizing surfaces
• The singular set of J-holomorphic maps into projective algebraic varieties
• Currents in metric spaces

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