A note on the singular set of area-minimizing hypersurfaces

DOI10.1007/s00526-019-1660-7zbMath1429.53012OpenAlexW2992089261MaRDI QIDQ2279703

Nick Edelen

Publication date: 13 December 2019

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://hdl.handle.net/1721.1/131358

zbMATH Keywords

\((n-7)\)-dimensional measureisoperimetric-type bound

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Variational problems in a geometric measure-theoretic setting (49Q20) Geometric measure and integration theory, integral and normal currents in optimization (49Q15)

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Cites Work

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• Stable embedded minimal surfaces bounded by a straight line
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• Singularities of energy minimizing maps from the ball to the sphere: Examples, counterexamples, and bounds
• Regularity theory for almost minimal currents
• Rectifiability of the singular set of energy minimizing maps
• On the first variation of a varifold
• Optimal interior and boundary regularity for almost minimizers to elliptic variational integrals
• Quantitative stratification for some free-boundary problems
• Boundary regularity and embedded solutions for the oriented Plateau problem

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