Rectifiability and upper Minkowski bounds for singularities of harmonic \(Q\)-valued maps

DOI10.4171/CMH/449zbMath1408.49045arXiv1612.01813MaRDI QIDQ1757306

Andrea Marchese, Daniele Valtorta, Camillo De Lellis, Emanuele Nunzio Spadaro

Publication date: 3 January 2019

Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.01813

zbMATH Keywords

regularitysingularitiesDirichlet energyrectifiabilitymultiple-valued functions

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Variational problems in a geometric measure-theoretic setting (49Q20) Regularity of solutions in optimal control (49N60)

Related Items (12)

Rectifiability of the singular set of harmonic maps into buildings ⋮ Boundary unique continuation on \(C^1\)-dini domains and the size of the singular set ⋮ Defects of liquid crystals with variable degree of orientation ⋮ Multiple valued Jacobi fields ⋮ Unique continuation on convex domains ⋮ How a minimal surface leaves a thin obstacle ⋮ 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 ⋮ Rectifiability of line defects in liquid crystals with variable degree of orientation ⋮ Quantitative stratification for some free-boundary problems ⋮ On the measure and the structure of the free boundary of the lower dimensional obstacle problem ⋮ Branch points for (almost-)minimizers of two-phase free boundary problems

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