Books, Proceedings and Seminars of Centre Mersenne

[1] W. K. Allard – « On boundary regularity for Plateau’s problem », Bulletin of the American Mathematical Society 75 (1969), no. 3, p. 522–523. | DOI | Zbl

[2] —, « On the first variation of a varifold », Annals of mathematics 95 (1972), no. 3, p. 417–491. | DOI | Zbl

[3] —, « On the first variation of a varifold: Boundary behavior », Annals of Mathematics 101 (1975), no. 3, p. 418–446. | DOI | Zbl

[4] F. J. Almgren – Almgren’s big regularity paper: $Q$-valued functions minimizing Dirichlet’s integral and the regularity of area-minimizing rectifiable currents up to codimension $2$. Edited by V. Scheffer and J. E. Taylor, World Sci. Monogr. Ser. Math., vol. 1, World scientific, Singapore, 2000. | Zbl

[5] J. Azzam & X. Tolsa – « Characterization of $n$-rectifiability in terms of Jones’ square function: Part II », Geometric and Functional Analysis 25 (2015), no. 5, p. 1371–1412. | DOI | Zbl

[6] M. Badger, M. Engelstein & T. Toro – « Slowly vanishing mean oscillations: Non-uniqueness of blow-ups in a two-phase free boundary problem », Vietnam Journal of Mathematics 52 (2024), no. 3, p. 615–625. | DOI | Zbl

[7] E. Bombieri, E. De Giorgi & E. Giusti – « Minimal cones and the Bernstein problem », Inventiones mathematicae 7 (1969), p. 243–268. | DOI | Zbl

[8] E. Bombieri – « Regularity theory for almost minimal currents », Arch. Rational Mech. Anal. 78 (1982), no. 2, p. 99–130. | DOI | Zbl

[9] S. X.-D. Chang – « Two-dimensional area minimizing integral currents are classical minimal surfaces », Journal of the American Mathematical Society 1 (1988), no. 4, p. 699–778. | DOI | Zbl

[10] E. De Giorgi – « Nuovi teoremi relativi alle misure $(r-1)$-dimensionali in uno spazio ad $r$-dimensioni », Ricerche Mat. 4 (1955), p. 95–113. | Zbl

[11] C. De Lellis – « The size of the singular set of area-minimizing currents », in Surveys in differential geometry 2016. Advances in geometry and mathematical physics, Surv. Differ. Geom., vol. 21, Int. Press, Somerville, MA, 2016, p. 1–83. | DOI | Zbl

[12] C. De Lellis & I. Fleschler – « An elementary rectifiability lemma and some applications », 2023. | arXiv

[13] C. De Lellis, P. Minter & A. Skorobogatova – « The fine structure of the singular set of area-minimizing integral currents III: Frequency 1 flat singular points and ${\mathscr{H}}^{m-2}$-a.e. uniqueness of tangent cones », 2023. | arXiv

[14] C. De Lellis, S. Nardulli & S. Steinbrüchel – « Uniqueness of boundary tangent cones for 2-dimensional area-minimizing currents », Nonlinear Analysis 230 (2023), p. 113235. | DOI | MR | Zbl

[15] —, « An allard-type boundary regularity theorem for 2d-minimizing currents at smooth curves with arbitrary multiplicity », Publications mathématiques de l’IHÉS 140 (2024), no. 1, p. 37–154. | DOI | Zbl

[16] C. De Lellis & A. Skorobogatova – « The fine structure of the singular set of area-minimizing integral currents I: the singularity degree of flat singular points », 2023. | arXiv

[17] —, « The fine structure of the singular set of area-minimizing integral currents II: rectifiability of flat singular points with singularity degree larger than $1$ », 2023, to appear in Commentarii Mathematici Helvetici. | arXiv

[18] C. De Lellis & E. Spadaro – $Q$-valued functions revisited, vol. 211, Mem. Amer. Math. Soc., no. 991, American Mathematical Society, Providence, RI, 2011. | DOI

[19] —, « Regularity of area minimizing currents I: gradient $L^p$ estimates », Geometric and Functional Analysis 24 (2014), no. 6, p. 1831–1884. | DOI | Zbl

[20] —, « Multiple valued functions and integral currents », Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 14 (2015), no. 4, p. 1239–1269. | DOI | Zbl

[21] —, « Regularity of area minimizing currents II: center manifold », Annals of Mathematics (2016), p. 499–575. | DOI | Zbl

[22] —, « Regularity of area minimizing currents III: blow-up », Annals of Mathematics (2016), p. 577–617. | DOI | Zbl

[23] C. De Lellis, E. Spadaro & L. Spolaor – « Regularity theory for 2-dimensional almost minimal currents II: branched center manifold », Annals of PDE 3 (2017), p. 1–85. | DOI | MR | Zbl

[24] —, « Uniqueness of tangent cones for two-dimensional almost-minimizing currents », Communications on Pure and Applied Mathematics 70 (2017), no. 7, p. 1402–1421. | DOI | MR | Zbl

[25] —, « Regularity theory for 2-dimensional almost minimal currents I: Lipschitz approximation », Transactions of the American Mathematical Society 370 (2018), no. 3, p. 1783–1801. | DOI | MR | Zbl

[26] —, « Regularity theory for $2$-dimensional almost minimal currents III: Blowup », Journal of Differential Geometry 116 (2020), no. 1, p. 125–185. | DOI | MR | Zbl

[27] G. De Philippis & E. Paolini – « A short proof of the minimality of Simons cone », Rendiconti del Seminario Matematico della Università di Padova 121 (2009), p. 233–241. | DOI | MR | Zbl

[28] A. Doan, E.-N. Ionel & T. Walpuski – « The Gopakumar-Vafa finiteness conjecture », 2021. | arXiv

[29] A. Doan & T. Walpuski – « Castelnuovo’s bound and rigidity in almost complex geometry », Adv. Math. 379 (2021), article no. 107550 (23 pages). | DOI | Zbl

[30] J. Douglas – « Minimal surfaces of higher topological structure », Proceedings of the National Academy of Sciences of the United States of America 24 (1938), no. 8, p. 343–353. | DOI | Zbl

[31] H. Federer – « The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension », Bull. Amer. Math. Soc 76 (1970), p. 767–771. | DOI | Zbl

[32] H. Federer & W. H. Fleming – « Normal and integral currents », Annals of Mathematics 72 (1960), no. 3, p. 458–520. | DOI | Zbl

[33] I. Fleschler – « On the uniqueness of tangent cones to area minimizing currents at boundaries with arbitrary multiplicity », 2024. | arXiv

[34] —, « An essential one sided boundary singularity for a $3$-dimensional area minimizing current in ${ℝ}^5$ », 2025. | arXiv

[35] I. Fleschler & R. Resende – « On the regularity of area minimizing currents at boundaries with arbitrary multiplicity », 2024. | arXiv

[36] N. Garofalo & F. Lin – « Monotonicity properties of variational integrals, $A_p$ weights and unique continuation », Indiana University Mathematics Journal 35 (1986), p. 245–268. | DOI | Zbl

[37] M. Goering & A. Skorobogatova – « Flat interior singularities for area almost-minimizing currents », 2023. | arXiv

[38] M. Grana – « Flux compactifications in string theory: a comprehensive review », Phys. Rep. 423(3) (2006), p. 91–158. | DOI

[39] J. Gutowski – « Generalized calibrations », in Progress in string theory and M-theory (Cargèse, 1999), NATO Sci. Ser. C Math. Phys. Sci., vol. 564, 2001, p. 343–346. | DOI | Zbl

[40] J. Gutowski, G. Papadopoulos & P. K. Townsend – « Supersymmetry and generalized calibrations », Phys. Rev. D (3) 60(10) (1999), article no. 106006 (11 pages). | DOI

[41] R. Hardt & L. Simon – « Boundary regularity and embedded solutions for the oriented plateau problem », Annals of Mathematics 110 (1979), no. 3, p. 439–486. | DOI | Zbl

[42] J. Harrison & H. Pugh – « Solutions to the Reifenberg Plateau problem with cohomological spanning conditions », Calc. Var. Partial Differential Equations 55 (2016), no. 4, article no. 87 (37 pages). | DOI | Zbl

[43] R. Harvey & J. Lawson, H. Blaine – « Calibrated geometries », Acta Math. 148 (1982), p. 47–157. | DOI | Zbl

[44] D. D. Joyce – Riemannian holonomy groups and calibrated geometry, Oxford Graduate Texts in Mathematics, vol. 12, Oxford University Press, Oxford, 2007. | Zbl

[45] Z. Liu – « On a conjecture of almgren: area-minimizing surfaces with fractal singularities », 2021. | arXiv

[46] —, « Homologically area-minimizing surfaces that cannot be calibrated », 2023. | arXiv

[47] P. Minter, D. Parise, A. Skorobogatova & L. Spolaor – « Rectifiability of the singular set and uniqueness of tangent cones for semicalibrated currents », 2024. | arXiv

[48] A. Naber & D. Valtorta – « Rectifiable-Reifenberg and the regularity of stationary and minimizing harmonic maps », Annals of Mathematics 185 (2017), no. 1, p. 131–227. | DOI | Zbl

[49] T. Radó – « On Plateau’s problem », Annals of Mathematics 31 (1930), no. 3, p. 457–469. | DOI

[50] E. R. Reifenberg – « Solution of the Plateau problem for $m$-dimensional surfaces of varying topological type », Acta Mathematica 104 (1960), no. 1, p. 1–92. | DOI | Zbl

[51] L. Simon – Lectures on geometric measure theory, Proceedings of the Centre for Mathematical Analysis, Australian National University, vol. 3, Australian National University, Centre for Mathematical Analysis, Canberra, 1983. | Zbl

[52] —, « Cylindrical tangent cones and the singular set of minimal submanifolds », Journal of Differential Geometry 38 (1993), no. 3, p. 585–652. | DOI | Zbl

[53] —, « Rectifiability of the singular sets of multiplicity 1 minimal surfaces and energy minimizing maps », Surveys in differential geometry 2 (1993), no. 1, p. 246–305. | DOI | Zbl

[54] —, « Stable minimal hypersurfaces in ${ℝ}^{N+1+\ell }$ with singular set an arbitrary closed $K\subset \left\{0\right\}\times {ℝ}^{\ell }$ », Annals of Mathematics 197 (2023), no. 3, p. 1205–1234. | DOI | Zbl

[55] L. Spolaor – « Almgren’s type regularity for semicalibrated currents », Advances in Mathematics 350 (2019), p. 747–815. | DOI | Zbl

[56] A. Strominger, S.-T. Yau & E. Zaslow – « Mirror symmetry is t-duality », Nuclear Phys. B 479(1-2) (1996), p. 243–259. | DOI | Zbl

[57] G. Tian – « Gauge theory and calibrated geometry. I », Ann. of Math. (2) 151 (2000), no. 1, p. 193–268. | DOI | Zbl

[58] B. White – « Tangent cones to two-dimensional area-minimizing integral currents are unique », Duke Math. J. 50 (1983), no. 1, p. 143–160. | DOI | Zbl

[59] N. Wickramasekera – « A general regularity theory for stable codimension 1 integral varifolds », Annals of mathematics (2014), p. 843–1007. | DOI | Zbl