Open Access
Volume 27, 2021
Article Number 34
Number of page(s) 30
Published online 30 April 2021
  1. E. Akhmetgaliyev, C.-Y. Kao and B. Osting, Computational methods for extremal Steklov problems. SIAM J. Cont. Optim. 55 (2017) 1226–1240 [Google Scholar]
  2. W. Alhejaili and C.-Y. Kao, Maximal convex combinations of sequential Steklov eigenvalues. J. Scientific Computing 79 (2019) 2006–2026 [Google Scholar]
  3. P.R.S Antunes and P. Freitas, Numerical optimization of low eigenvalues of the Dirichlet and Neumann Laplacians. J. Optim. Theory Appl. 154 (2012) 235–257 [Google Scholar]
  4. P.R.S. Antunes and E. Oudet, Numerical minimization of Dirichlet Laplacian eigenvalues of four-dimensional geometries. SIAM J. Sci. Comput. 39 (2017) B508–B521 [Google Scholar]
  5. B. Bogosel and E. Oudet, Qualitative and numerical analysis of a spectral problem with perimeter constraint. SIAM J. Cont. Optim. 54 (2016) 317–340 [Google Scholar]
  6. B. Bogosel, D. Bucur and A. Giacomini, Optimal shapes maximizing the Steklov eigenvalues. SIAM J. Math. Anal. 49 (2017) 1645–1680 [Google Scholar]
  7. K. Brown, Min-energy configurations of electrons on a sphere (2020). [Google Scholar]
  8. R.H. Byrd, J. Nocedal and R.A. Waltz, Knitro: An integrated package for nonlinear optimization, in Large-Scale Nonlinear Optimization. Springer (2006) 35–59 [Google Scholar]
  9. M. Dambrine, D. Kateb and J. Lamboley, An extremal eigenvalue problem for the Wentzell–Laplace operator. Annales de l’Institut Henri Poincaré (C) Non Linear Analysis 33 (2016) 409–445 [Google Scholar]
  10. B. Dittmar, Sums of reciprocal Stekloff eigenvalues. Math. Nachr. 268 (2004) 44–49 [Google Scholar]
  11. A. El Soufi, S. Ilias, et al., Domain deformations and eigenvalues of the Dirichlet Laplacian in a Riemannian manifold. Ill. J. Math. 51 (2007) 645–666 [Google Scholar]
  12. X.-Q. Fan, L.-F. Tam and C. Yu, Extremal problems for Steklov eigenvalues on annuli. Cal. Var. Part. Diff. Equ. 54 (2014) 1043–1059 [Google Scholar]
  13. M. Fekete, über die verteilung der wurzeln bei gewissen algebraischen gleichungen mit ganzzahligen koeffizienten. Math. Z. 17 (1923) 228–249 [Google Scholar]
  14. A. Fraser and R. Schoen, The first Steklov eigenvalue, conformal geometry and minimal surfaces. Adv. Math. 226 (2011) 4011–4030 [Google Scholar]
  15. A. Fraser and R. Schoen, Minimal surfaces and eigenvalue problems. Contemp. Math. (2013) 105–121. doi:10.1090/conm/ 599/11927. [Google Scholar]
  16. A. Fraserand R. Schoen, Sharp eigenvalue bounds and minimal surfaces in the ball. Invent Math. 203 (2015) 823–890 [Google Scholar]
  17. A. Fraser and R. Schoen, Some results on higher eigenvalue optimization. Cal. Var. Part. Diff. Equ. 59 (2020) 1–22 [Google Scholar]
  18. F. Gardiner and N. Lakic, Quasiconformal Teichmüller Theory. American Mathematical Society (1999) [Google Scholar]
  19. A. Girouard and J. Lagacé, Large Steklov eigenvalues via homogenisation on manifolds. Preprint, arXiv:2004.04044 (2020). [Google Scholar]
  20. A. Girouard, R.S. Laugesen and B.A. Siudeja, Steklov eigenvalues and quasiconformal maps of simply connected planar domains. Arch. Rat. Mech. Anal. 219 (2016) 903–936 [Google Scholar]
  21. A. Girouard and I. Polterovich, Upper bounds for Steklov eigenvalues on surfaces. Electron. Res. Announ. Math. Sci. 19 (2012) 77–85 [Google Scholar]
  22. A. Girouard and I. Polterovich, Spectral geometry of the Steklov problem. J. Spectr. Theory 7 (2017) 321–359 [Google Scholar]
  23. P. Henrici, Applied and Computational Complex Analysis. John Wiley & Sons (1986) [Google Scholar]
  24. M. Jin, X. Gu, Y. He and Y. Wang, Conformal Geometry. Springer International Publishing (2018) [Google Scholar]
  25. C.-Y. Kao, R. Lai and B. Osting, Maximization of Laplace-Beltrami eigenvalues on closed Riemannian surfaces. ESAIM: COCV 23 (2017) 685–720 [CrossRef] [EDP Sciences] [Google Scholar]
  26. M. Karpukhin, Bounds between Laplace and Steklov eigenvalues on nonnegatively curved manifolds. Electron. Res. Announ. Math. Sci. 24 (2017) 100–109 [Google Scholar]
  27. P.D. Lamberti and L. Provenzano, Viewing the Steklov eigenvalues of the Laplace operator as critical Neumann eigenvalues, in Trends in Mathematics. Springer International Publishing (2015) 171–178 [Google Scholar]
  28. M. Li, Free boundary minimal surfaces in the unit ball: recent advances and open questions. Preprint, arXiv:1907.05053 (2019). [Google Scholar]
  29. É. Martel, Le spectre de Steklov de la boule trou’ee. J. des étudiants de 1er cycle en mathématiques de l’Université Laval (2014) [Google Scholar]
  30. H. Matthiesen and R. Petrides, Free boundary minimal surfaces of any topological type in Euclidean balls via shape optimization. Preprint, arXiv:2005.06051 (2020). [Google Scholar]
  31. P.J. Olver, Complex Analysis and Conformal Mapping. University of Minnesota (2017) [Google Scholar]
  32. B. Osting, Optimization of spectral functions of Dirichlet–Laplacian eigenvalues. J. Computat. Phys 229 (2010) 8578–8590 [Google Scholar]
  33. B. Osting and C.-Y. Kao, Minimal convex combinations of sequential Laplace–Dirichlet eigenvalues. SIAM J. Sci. Comput. 35 (2013) B731–B750 [Google Scholar]
  34. B. Ostingand C.-Y. Kao, Minimal convex combinations of three sequential Laplace-Dirichlet eigenvalues. Appl. Math. Optim. 69 (2014) 123–139 [Google Scholar]
  35. É. Oudet, Numerical minimization of eigenmodes of a membrane with respect to the domain. ESAIM: COCV 10 (2004) 315–330 [CrossRef] [EDP Sciences] [Google Scholar]
  36. É. Oudet, Personal website (2020).˙n.php [Google Scholar]
  37. L.N. Trefethen, Series solution of Laplace problems. ANZIAM J 60 (2018) 1–26 [Google Scholar]
  38. M. Weber, Bloomington’s virtual minimal surface museum (2020). [Google Scholar]
  39. R. Weinstock, Inequalities for a classical eigenvalue problem. Indiana Univ. Math. J. 3 (1954) 745–753 [Google Scholar]
  40. W. Zeng, X. Yin, M. Zhang, F. Luo and X. Gu, Generalized Koebe’s method for conformal mapping multiply connected domains, in 2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling (2009) 89–100. doi:10.1145/1629255.1629267. [Google Scholar]

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