Stratification for the singular set of approximate harmonic maps

DOI10.1007/s00209-018-2068-3zbMath1408.58012arXiv1611.03008OpenAlexW3102216378WikidataQ125118095 ScholiaQ125118095MaRDI QIDQ1794592

Daniele Valtorta, Aaron Naber

Publication date: 15 October 2018

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.03008

zbMATH Keywords

rectifiable setquantitative stratificationapproximate harmonic mapReifenberg theorem

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Harmonic maps, etc. (58E20) Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects) (32S60)

Related Items

Boundary unique continuation on \(C^1\)-dini domains and the size of the singular set, Regularity of the free boundary for the vectorial Bernoulli problem, Quantitative stratification for some free-boundary problems, Rectifiability and upper Minkowski bounds for singularities of harmonic \(Q\)-valued maps, Quantitative regularity for \(p\)-minimizing maps through a Reifenberg theorem, Regularity of Dirac-harmonic maps with \(\lambda\)-curvature term in higher dimensions, Rectifiability of the singular set of multiple-valued energy minimizing harmonic maps

Cites Work

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• Improved estimate of the singular set of Dir-minimizing \(Q\)-valued functions via an abstract regularity result
• Rectifiable-Reifenberg and the regularity of stationary and minimizing harmonic maps
• Solution of the Plateau problem for \(m\)-dimensional surfaces of varying topological type
• Quantitative stratification and higher regularity for biharmonic maps
• Characterization of \(n\)-rectifiability in terms of Jones' square function. II
• Gradient estimates and blow-up analysis for stationary harmonic maps
• On the singular set of stationary harmonic maps
• Geometric conditions and existence of bi-Lipschitz parameterizations
• Geometry of harmonic maps
• Lower bounds on Ricci curvature and quantitative behavior of singular sets
• Quantitative stratification and the regularity of mean curvature flow
• Reifenberg parameterizations for sets with holes
• Minimizing p-harmonic maps into spheres.
• Nonstationary weak limit of a stationary harmonic map sequence
• Compactness properties of weakly p-harmonic maps into homogeneous spaces
• Quantitative Stratification and the Regularity of Harmonic Maps and Minimal Currents
• Critical Sets of Elliptic Equations
• Characterization of \(n\)-rectifiability in terms of Jones' square function. I