A direct approach to the anisotropic Plateau problem

References

[1] W. K. Allard, A characterization of the area integrand, Symposia Mathematica. Vol. XIV (Convegni 1973), Academic Press, London (1974), 429–444. Suche in Google Scholar

[2] F. J. Almgren, Jr., Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and singularity structure, Ann. of Math. (2) 87 (1968), 321–391. 10.2307/1970587Suche in Google Scholar

[3] F. J. Almgren, Jr., Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints, Mem. Amer. Math. Soc. 4 (1976), no. 165. 10.1090/memo/0165Suche in Google Scholar

[4] L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford Math. Monogr., Clarendon Press, New York, 2000. 10.1093/oso/9780198502456.001.0001Suche in Google Scholar

[5] G. David, Should we solve Plateau’s problem again?, Advances in Analysis: The Legacy of Elias M. Stein, Princeton Math. Ser. 50, Princeton University Press, Princeton (2014), 108–145. 10.23943/princeton/9780691159416.003.0006Suche in Google Scholar

[6] G. David and S. Semmes, Uniform rectifiability and quasiminimizing sets of arbitrary codimension, Mem. Amer. Math. Soc. 144 (2000), no. 687. 10.1090/memo/0687Suche in Google Scholar

[7] E. De Giorgi, Su una teoria generale della misura (r-1)-dimensionale in uno spazio ad r dimensioni, Ann. Mat. Pura Appl. (4) 36 (1954), 191–213. 10.1007/BF02412838Suche in Google Scholar

[8] C. De Lellis, Rectifiable Sets, Densities and Tangent Measures, Zur. Lect. Adv. Math., European Mathematical Society (EMS), Zürich, 2008. 10.4171/044Suche in Google Scholar

[9] C. De Lellis, F. Ghiraldin and F. Maggi, A direct approach to Plateau’s problem, J. Eur. Math. Soc. (JEMS) 19 (2017), 2219–2240. 10.4171/JEMS/716Suche in Google Scholar

[10] G. De Philippis, A. De Rosa and F. Ghiraldin, A direct approach to Plateau’s problem in any codimension, Adv. Math. 288 (2016), 59–80. 10.1016/j.aim.2015.10.007Suche in Google Scholar

[11] G. De Philippis, A. De Rosa and F. Ghiraldin, Rectifiability of varifolds with locally bounded first variation with respect to anisotropic surface energies, preprint (2016), https://arxiv.org/abs/1609.01908; to appear in Comm. Pure Appl. Math. 10.1002/cpa.21713Suche in Google Scholar

[12] G. De Philippis, A. De Rosa and F. Ghiraldin, Existence results for minimizers of parametric elliptic functionals, preprint (2017), https://arxiv.org/abs/1704.07801. 10.1007/s12220-019-00165-8Suche in Google Scholar

[13] Y. Fang, Existence of minimizers for the Reifenberg Plateau problem, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 16 (2016), no. 3, 817–844. 10.2422/2036-2145.201407_008Suche in Google Scholar

[14] H. Federer, Geometric Measure Theory, Grundlehren Math. Wiss. 153, Springer, Berlin, 1969. Suche in Google Scholar

[15] H. Federer and W. H. Fleming, Normal and integral currents, Ann. of Math. (2) 72 (1960), 458–520. 10.2307/1970227Suche in Google Scholar

[16] V. Feuvrier, Condensation of polyhedric structures onto soap films, preprint (2009), https://arxiv.org/abs/0906.3505. Suche in Google Scholar

[17] J. Harrison and H. Pugh, Existence and soap film regularity of solutions to Plateau’s problem, Adv. Calc. Var. 9 (2016), no. 4, 357–394. 10.1515/acv-2015-0023Suche in Google Scholar

[18] J. Harrison and H. Pugh, Solutions to the Reifenberg Plateau problem with cohomological spanning conditions, Calc. Var. Partial Differential Equations 55 (2016), no. 4, Article ID 87. 10.1007/s00526-016-1022-7Suche in Google Scholar

[19] J. Harrison and H. Pugh, General methods of elliptic minimization, preprint (2017), https://arxiv.org/abs/1603.04492v3. 10.1007/s00526-017-1217-6Suche in Google Scholar

[20] P. Mattila, Geometry of Sets and Measures in Euclidean Spaces, Cambridge Stud. Adv. Math. 44, Cambridge University Press, Cambridge, 1995. 10.1017/CBO9780511623813Suche in Google Scholar

[21] C. B. Morrey, Jr., Multiple Integrals in the Calculus of Variations, Grundlehren Math. Wiss. 130, Springer, Berlin, 1966. 10.1007/978-3-540-69952-1Suche in Google Scholar

[22] D. Preiss, Geometry of measures in ℝn: Distribution, rectifiability, and densities, Ann. of Math. (2) 125 (1987), no. 3, 537–643. 10.2307/1971410Suche in Google Scholar

[23] E. R. Reifenberg, Solution of the Plateau Problem for m-dimensional surfaces of varying topological type, Acta Math. 104 (1960), 1–92. 10.1007/BF02547186Suche in Google Scholar

[24] L. Simon, Lectures on Geometric Measure Theory, Proc. Centre Math. Anal. Austral. Nat. Univ. 3, Australian National University, Centre for Mathematical Analysis, Canberra, 1983. Suche in Google Scholar