On the Size of the Singular Set of Minimizing Harmonic Maps

Katarzyna Mazowiecka, University of Warsaw, Warszawa, Poland, Michal Miskiewicz, Polish Academy of Sciences, Warszawa, Poland, and University of Warsaw, Warszawa, Poland, and Armin Schikorra, University of Pittsburgh, Pennsylvania

1. Introduction 2. Partial regularity in the interior 3. Monotonicity formula and tangent maps at the boundary 4. Refined estimates by Naber and Valtorta 5. Extension property and its consequences 6. Strong convergence for minimizers and its consequences 7. Boundary regularity for smooth and singular boundary data in $W^{1,n-1}$ 8. Hardt and Lin's stability of singularities for $n \geq 3$ 9. Almgren and Lieb's linear law: Size of the singular set 10. Final remarks A. Trace theorems