The singular structure and regularity of stationary varifolds

DOI10.4171/JEMS/987zbMath1460.35143arXiv1505.03428MaRDI QIDQ2216737

Daniele Valtorta, Aaron Naber

Publication date: 17 December 2020

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.03428

zbMATH Keywords

singularitiesmean curvaturevarifoldsquantitative stratificationminimal currents

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Nonlinear elliptic equations (35J60) Currents in global analysis (58A25)

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Cites Work

• Unnamed Item
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• Unnamed Item
• 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
• Cylindrical tangent cones and the singular set of minimal submanifolds
• Lower bounds on Ricci curvature and quantitative behavior of singular sets
• Quantitative stratification and the regularity of harmonic map flow
• Quantitative stratification and the regularity of mean curvature flow
• Some interior regularity theorems for minimal surfaces and an extension of Bernstein's theorem
• Minimal varieties in Riemannian manifolds
• Minimal cones and the Bernstein problem
• Normal and integral currents
• On the first variation of a varifold
• Reifenberg parameterizations for sets with holes
• Quantitative Stratification and the Regularity of Harmonic Maps and Minimal Currents
• Volume Estimates on the Critical Sets of Solutions to Elliptic PDEs
• Critical Sets of Elliptic Equations
• The size of the singular set of area-minimizing currents
• Characterization of \(n\)-rectifiability in terms of Jones' square function. I

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