Citation: |
[1] |
A. D. Alexandrov, Uniqueness theorems for surfaces in the large, I. (Russian) Vestnik Leningrad Univ. Math., 11 (1956), 5-17. |
[2] |
O. Druet, Asymptotic expansion of the Faber-Krahn profile of a compact Riemannian manifold, C. R. Math. Acad. Sci. Paris, 346 (2008), 1163-1167.doi: 10.1016/j.crma.2008.09.022. |
[3] |
A. El Soufi and S. Ilias, Domain deformations and eigenvalues of the Dirichlet Laplacian in Riemannian manifold, Illinois J. Math., 51 (2007), 645-666. |
[4] |
G. Faber, Beweis, dass unter allen homogenen Membranen von gleicher Fläche und gleicher Spannung die kreisförmige den tiefsten Grundton gibt, Sitzungsber. - Bayer. Akad. Wiss. München, Math.-Phys. Kl., (1923), 169-172. |
[5] |
P. R. Garadedian and M. Schiffer, Variational problems in the theory of elliptic partial differetial equations, J. Rat. Mech. An., 2 (1953), 137-171. |
[6] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Grundlehren der mathematischen Wissenschaften, a Series of Comprehensive Studies in Mathematics, Vol. 224, $2^{nd}$ Edition, Springer, 1983.doi: 10.1007/978-3-642-61798-0. |
[7] |
K. Gro$\beta$e-Brauckmann, New surfaces of constant mean curvature, Math. Z., 214 (1993), 527-565.doi: 10.1007/BF02572424. |
[8] |
D. Henry, Perturbation of the Boundary in Boundary-Value Problems of Partial Differential Equations, London Mathematical Society, Lecture Note Series, 318, Cambridge University Press, 2005.doi: 10.1017/CBO9780511546730. |
[9] |
L. Karp and M. Pinsky, The first eigenvalue of a small geodesic ball in a Riemannian manifold, Sci. Math. (2), 111 (1987), 229-239. |
[10] |
E. Krahn, Über eine von Raleigh formulierte Minimaleigenschaft der Kreise, Math. Ann., 94 (1925), 97-100.doi: 10.1007/BF01208645. |
[11] |
E. Krahn, Uber Minimaleigenschaften der Kugel in drei und mehr dimensionen, Acta Comm. Univ. Tartu (Dorpat), A9 (1926), 1-44. |
[12] |
T. Lang and R. Wong, "Best possible'' upper bounds for the first two positive zeros of the Bessel function $J_\nu(x)$: The infinite case, J. Comput. Appl. Math., 71 (1996), 311-329.doi: 10.1016/0377-0427(95)00220-0. |
[13] |
J. M. Lee and T. H. Parker, The Yamabe Problem, Bulletin of the American Mathematical Society, 17 (1987), 37-91.doi: 10.1090/S0273-0979-1987-15514-5. |
[14] |
S. Nardulli, The isoperimetric profile of a smooth Riemannian manifold for small volumes, Ann. Global Anal. Geom., 36 (2009), 111-131.doi: 10.1007/s10455-008-9152-6. |
[15] |
F. Pacard and P. Sicbaldi, Extremal domains for the first eigenvalue of the Laplace-Beltrami operator, Ann. Inst. Fourier, 59 (2009), 515-542.doi: 10.5802/aif.2438. |
[16] |
F. Pacard and X. Xu, Constant mean curvature sphere in Riemannian manifolds, Manuscripta Math., 128 (2009), 275-295.doi: 10.1007/s00229-008-0230-7. |
[17] |
M. Ritoré, Superficies Con Curvatura Media Constante, Tesis doctoral, Universidad de Granada, 1994. |
[18] |
M. Ritoré, Examples of constant mean curvature surfaces obtained from harmonic maps to the two sphere, Math. Z., 226 (1997), 127-146.doi: 10.1007/PL00004326. |
[19] |
A. Ros and P. Sicbaldi, Geometry and Topology for some overdetermined elliptic problems, J. Diff. Eq., 255 (2013), 951-977.doi: 10.1016/j.jde.2013.04.027. |
[20] |
F. Schlenk and P. Sicbaldi, Bifurcating extremal domains for the first eigenvalue of the Laplacian, Adv. Math., 229 (2012), 602-632.doi: 10.1016/j.aim.2011.10.001. |
[21] |
R. Schoen and S. T. Yau, Lectures on Differential Geometry, International Press, 1994. |
[22] |
J. Serrin, A symmetry problem in potential theory, Arch. Rational Mech. Anal., 43 (1971), 304-318. |
[23] |
P. Sicbaldi, Extremal domains of big volume for the first eigenvalue of the Laplace-Beltrami operator in a compact manifold, Ann. Inst. Poincaré (C) An. non linéaire, 31 (2014), 1231-1265.doi: 10.1016/j.anihpc.2013.09.001. |
[24] |
T. J. Willmore, Riemannian Geometry, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1993. |
[25] |
R. Ye, Foliation by constant mean curvature spheres, Pacific J. Math., 147 (1991), 381-396.doi: 10.2140/pjm.1991.147.381. |