Regularity of area minimizing currents mod \(p\)

DOI10.1007/s00039-020-00546-0zbMath1456.49032arXiv1909.05172OpenAlexW3094678175MaRDI QIDQ2216464

Salvatore Stuvard, Andrea Marchese, Camillo De Lellis, Jonas Hirsch

Publication date: 16 December 2020

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

Full work available at URL: https://arxiv.org/abs/1909.05172

zbMATH Keywords

minimal surfacescenter manifoldregularity theoryblow-up analysismultiple valued functionsarea minimizing currents mod(p)

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Minimal surfaces and optimization (49Q05) 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) Length, area, volume, other geometric measure theory (28A75) Second-order elliptic systems (35J47)

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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
• Some basic theorems on flat \(G\) chains
• The structure of minimizing hypersurfaces mod 4
• Regularity and singularity estimates on hypersurfaces minimizing parametric elliptic variational integrals
• Cylindrical tangent cones and the singular set of minimal submanifolds
• On the structure of flat chains modulo \(p\)
• Quantitative nonorientability of embedded cycles
• Regularity of the singular sets of two-dimensional area-minimizing flat chains modulo 3 in R\(^3\)
• Almgren's type regularity for semicalibrated currents
• On the first variation of a varifold
• Multiple valued functions and integral currents
• Rectifiable and flat <i>G</i> chains in a metric space
• 𝑄-valued functions revisited
• Stratification of minimal surfaces, mean curvature flows, and harmonic maps.
• The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension
• Currents in metric spaces
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