A note on the singular set of area-minimizing hypersurfaces

Allard, W.: On the first variation of a varifold. Ann. Math. 2(95), 417–491 (1972)MathSciNetCrossRefGoogle Scholar

Almgren Jr., F.J.: Optimal isoperimetric inequalities. Indiana Univ. Math. J. 35, 451–547 (1986)MathSciNetCrossRefGoogle Scholar

Almgren, F.J., Lieb, Elliott H.: Singularities of energy minimizing maps from the ball to the sphere: examples, counterexamples, and bounds. Ann. Math. 128(3), 483–530 (1988)MathSciNetCrossRefGoogle Scholar

Bombieri, E.: Regularity theory for almost minimal currents. Arch. Rational Mech. Anal. 78, 99–130 (1982)MathSciNetCrossRefGoogle Scholar

Duzaar, F., Steffan, K.: Optimal interior and boundary regularity for almost minimizers to elliptic variational integrals. J. Reine Angew. Math. 546, 73–138 (2002)MathSciNetzbMATHGoogle Scholar

Edelen, N., Engelstein, M.: Quantitative stratification for some free-boundary problems. Trans. Am. Math. Soc. (2017)Google Scholar

Edelen, N.: Notes on a measure theoretic version of Naber–Valtorta’s rectifiability theorem. http://math.mit.edu/~edelen/general-nv.pdf. Accessed 10 Jan 2019

Gruter, M.: Optimal regularity for codimension one minimal surfaces with a free-boundary. Manuscr. Math. 58, 295–343 (1987)MathSciNetCrossRefGoogle Scholar

Gruter, M., Jost, J.: Allard type regularity results for varifolds with free boundaries. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 13, 129–169 (1986)MathSciNetzbMATHGoogle Scholar

Hardt, R., Simon, L.: Boundary regularity and embedded solutions for the oriented plateau problem. Ann. Math. 2(110), 439–486 (1979)MathSciNetCrossRefGoogle Scholar

Mazowiecka, K., Miskiewicz, M., Schikorra, A.: On the size of the singular set of minimizing harmonic maps into the sphere in dimension three (2018). arXiv:1811.00515

Mazowiecka, K, Miskiewicz, M., Schikorra, A.: On the size of the singular set of minimizing harmonic maps into a \(2\) sphere in dimension four and higher (2018). arXiv:1902.03161

Naber, A., Valtorta, D.: The singular structure and regularity of stationary and minimizing varifolds (2015). arXiv:1505.03428

Naber, A., Valtorta, D.: Rectifiable-reifenberg and the regularity of stationary and minimizing harmonic maps. Ann. Math. 2(185), 131–227 (2017)MathSciNetCrossRefGoogle Scholar

Perez, J.: Stable embedded minimal surfaces bounded by a straight line. Calc. Variations Partial Differ Equ 29, 267–279 (2007)MathSciNetCrossRefGoogle Scholar

Simon, L.: Lectures on geometric measure theory. In: Proceedings of the Centre for Mathematical Analysis, Australian National University, vol. 3. Australian National University, Centre for Mathematical Analysis, Canberra (1983)Google Scholar

Simon, L.: Rectifiability of the singular set of energy minimizing maps. Calc. Variations Partial Differ. Equ. 3, 1–65 (1995)MathSciNetCrossRefGoogle Scholar

White, B.: Half of Enneper’s surface minimizes area. In: Jost, J. (ed.) Geometric Analysis and the Calculus of Variations for Stefan Hildebrandt, pp. 361–367. International Press, Somerville (1996)Google Scholar