Open Access
Volume 25, 2019
Article Number 77
Number of page(s) 37
Published online 05 December 2019
  1. F.J. Almgren, Jr., Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints. Mem. Am. Math. Soc. 4 (1976) 165. [Google Scholar]
  2. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford Mathematical Monograph. The Clarendon Press, Oxford University Press, New York (2000). [Google Scholar]
  3. F. Cagnetti, M. Colombo, G. De Philippis and F. Maggi, Rigidity of equality cases in Steiner’s perimeter inequality. Anal. PDE 7 (2014) 1535–1593. [CrossRef] [Google Scholar]
  4. M. Chlebík, A. Cianchi and N. Fusco, The perimeter inequality under Steiner symmetrization: cases of equality. Ann. Math. 162 (2005) 525–555. [Google Scholar]
  5. J. Corneli, I. Corwin, S. Hurder, V. Sesum, Y. Xu, E. Adams, D. Davis, M. Lee, R. Visocchi and N. Hoffman, Double bubbles in Gauss space and spheres. Houston J. Math. 34 (2008) 181–204. [Google Scholar]
  6. J. Corneli, P. Holt, G. Lee, N. Leger, E. Schoenfeld and B. Steinhurst, The double bubble problem on the flat two-torus. Trans. Amer. Math. Soc. 356 (2004) 3769–3820. [CrossRef] [Google Scholar]
  7. A. Cotton and D. Freeman, The double bubble problem in spherical space and hyperbolic space. Int. J. Math. Math. Sci. 32 (2002) 641–699. [Google Scholar]
  8. R. Dorff, G. Lawlor, D. Sampson and B. Wilson, Proof of the planar double bubble conjecture using metacalibration methods. Involve 2 (2009) 611–628. [Google Scholar]
  9. L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions. Revised edition, Textbooks in Mathematics. CRC Press, Boca Raton, FL (2015). [Google Scholar]
  10. J. Foisy, M. Alfaro, J. Brock, N. Hodges and J. Zimba, The standard double soap bubble in R2 uniquely minimizes perimeter. Pacific J. Math. 159 (1993) 47–59. [CrossRef] [Google Scholar]
  11. V. Franceschi, A minimal partition problem with trace constraint in the Grushin plane. Calc. Var. Partial Differ. Equ. 56 (2017) 104. [Google Scholar]
  12. V. Franceschi and R. Monti, Isoperimetric problem in H-type groups and Grushin spaces. Rev. Mat. Iberoam. 32 (2016) 1227–1258. [CrossRef] [Google Scholar]
  13. J. Hass and R. Schlafly, Double bubbles minimize. Ann. Math. 151 (2000) 459–515. [Google Scholar]
  14. M. Hutchings, F. Morgan, M. Ritoré and A. Ros, Proof of the double bubble conjecture. Ann. Math. 155 (2002) 459–489. [Google Scholar]
  15. R. Lopez and T.B. Baker, The double bubble problem on the cone. N.Y. J. Math. 12 (2006) 157–167. [Google Scholar]
  16. F. Maggi, Sets of Finite Perimeter and Geometric Variational Problems. Vol. 135 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge (2012) [Google Scholar]
  17. J.D. Masters, The perimeter-minimizing enclosure of two areas in S2. Real Anal. Exchange 22 (1996/97) 645–654. [Google Scholar]
  18. R. Monti, Minimal surfaces and harmonic functions in the Heisenberg group, Nonlin. Anal. 126 (2015) 378–393. [CrossRef] [Google Scholar]
  19. R. Monti and D. Morbidelli, Isoperimetric inequality in the Grushin plane J. Geom. Anal. 14 (2004) 355–368. [Google Scholar]
  20. R. Monti and G. Stefani, Improved Lipschitz approximation of H-perimeter minimizing boundaries (English, with English and French summaries). J. Math. Pures Appl. 108 (2017) 372–398. [Google Scholar]
  21. R. Monti and D. Vittone, Height estimate and slicing formulas in the Heisenberg group. Anal. PDE 8 (2015) 1421–1454. [CrossRef] [Google Scholar]
  22. F. Morgan, Soap bubbles in R2 and in surfaces. Pacific J. Math. 165 (1994) 347–361. [CrossRef] [Google Scholar]
  23. F. Morgan, Geometric Measure Theory, 5th ed. Elsevier/ Press, Amsterdam (2016). [Google Scholar]
  24. P. Pansu, Une inégalité isopérimétrique sur le groupe de Heisenberg. C. R. Acad. Sci. Paris Sér. I Math. 295 (1982) 127–130. [Google Scholar]
  25. J.A.F. Plateau, Statique Expérimentale et Théorique des Liquides Soumis aux Seules Forces Moléculaires. Gauthier-Villars, Paris (1873). [Google Scholar]
  26. B.W. Reichardt, Proof of the double bubble conjecture in Rn. J. Geom. Anal. 18 (2008) 172–191. [Google Scholar]
  27. A. Ros, The isoperimetric problem, in Global Theory of Minimal Surfaces. Vol. 2 of Clay Mathematics Proceedings. American Mathematical Society, Providence, RI (2005) 175–209 [Google Scholar]
  28. J.E. Taylor, The structure of singularities in area-related variational problems with constraints. Bull. Amer. Math. Soc. 81 (1975) 1093–1095. [CrossRef] [Google Scholar]
  29. B. White, Regularity of the singular sets in immiscible fluid interfaces and solutions to other Plateau-type problems. Miniconference on geometry and partial differential equations. In Vol. 10 of Proceedings of the Centre Mathematical Analysis. The Australian National University, Canberra (1986) 244–249. [Google Scholar]
  30. W. Wichiramala, Proof of the planar triple bubble conjecture. J. Reine Angew. Math. 567 (2004) 1–49. [CrossRef] [Google Scholar]

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