J. Bourguignon, P. Li, and S. Yau, Upper bound for the first eigenvalue of algebraic submanifolds, Commentarii Mathematici Helvetici, vol.69, issue.1, pp.199-207, 1994.
DOI : 10.1007/BF02564482

P. Buser, M. Burger, and J. Dodziuk, Riemann surfaces of large genus and large ??1, Lecture Notes in Math, vol.64, pp.54-63, 1987.
DOI : 10.1090/conm/064/881458

Q. Cheng and H. Yang, Bounds on eigenvalues of Dirichlet Laplacian, Mathematische Annalen, vol.7, issue.1, pp.159-175, 2007.
DOI : 10.1007/s00208-006-0030-x

B. Colbois and J. Dodziuk, Riemannian Metrics with Large ?? 1, Proc. Amer, pp.905-906, 1994.
DOI : 10.2307/2160770

B. Colbois, E. B. Dryden, and A. E. Soufi, Extremal G-invariant eigenvalues of the Laplacian of G-invariant metrics, Mathematische Zeitschrift, vol.7, issue.1, pp.29-41, 2008.
DOI : 10.1007/s00209-007-0154-z

URL : https://hal.archives-ouvertes.fr/hal-00131806

B. Colbois and A. E. Soufi, Extremal eigenvalues of the Laplacian in a conformal class of metrics: the 'conformal spectrum, Annals of Global Analysis and Geometry, vol.24, issue.4, pp.337-349, 2003.
DOI : 10.1023/A:1026257431539

URL : https://hal.archives-ouvertes.fr/hal-00002872

B. Colbois and D. Maerten, Eigenvalues Estimate for the Neumann Problem of??a??Bounded Domain, Journal of Geometric Analysis, vol.36, issue.2, pp.1022-1032, 2008.
DOI : 10.1007/s12220-008-9041-z

A. Soufi and S. Ilias, Le volume conforme et ses applications d'après Li et Yau, Séminaire de Théorie Spectrale et Géométrie VII.1?VII.15. Univ. Grenoble I, Institut Fourier, 1983.

A. Soufi and S. Ilias, Immersions minimales, premi??re valeur propre du laplacien et volume conforme, Mathematische Annalen, vol.7, issue.2, pp.257-267, 1986.
DOI : 10.1007/BF01458460

A. Soufi and S. Ilias, Une in??galit?? du type ???Reilly??? pour les sous-vari??t??s de l'espace hyperbolique, Commentarii Mathematici Helvetici, vol.67, issue.1, pp.167-181, 1992.
DOI : 10.1007/BF02566494

A. El-soufi, H. Giacomini, and M. Jazar, A unique extremal metric for the least eigenvalue of the Laplacian on the Klein bottle, Duke Mathematical Journal, vol.135, issue.1, pp.181-202, 2006.
DOI : 10.1215/S0012-7094-06-13514-7

URL : https://hal.archives-ouvertes.fr/hal-00126909

A. El-soufi, M. Evans, I. Harrell, and S. Ilias, Universal inequalities for the eigenvalues of Laplace and Schr??dinger operators on submanifolds, Transactions of the American Mathematical Society, vol.361, issue.05, pp.2337-2350, 2009.
DOI : 10.1090/S0002-9947-08-04780-6

M. Engman, Sharp bounds for eigenvalues and multiplicities on surfaces of revolution, Pacific Journal of Mathematics, vol.186, issue.1, pp.29-37, 1998.
DOI : 10.2140/pjm.1998.186.29

J. Hass, J. H. Rubinstein, and A. Thompson, Knots and k-width. arXiv:math/0604256v1, 2006.
DOI : 10.1007/s10711-009-9368-z

URL : http://dx.doi.org/10.1007/s10711-009-9368-z

J. Hersch, Quatre propriétés isopérimétriques de membranes sphériques homogènes, C. R. Acad. Sci. Paris Sér. A-B, vol.270, pp.1645-1648, 1970.

M. W. Hirsch, Differential topology, Graduate Texts in Mathematics, vol.33, issue.33, 1976.
DOI : 10.1007/978-1-4684-9449-5

D. Jakobson, M. Levitin, N. Nadirashvili, N. Nigam, and I. Polterovich, How large can the first eigenvalue be on a surface of genus two? Int, Math. Res. Not, issue.63, pp.3967-3985, 2005.

D. Jakobson, N. Nadirashvili, and I. Polterovich, Extremal Metric for the First Eigenvalue on a Klein Bottle, Journal canadien de math??matiques, vol.58, issue.2, pp.381-400, 2006.
DOI : 10.4153/CJM-2006-016-0

N. Korevaar, Upper bounds for eigenvalues of conformal metrics, Journal of Differential Geometry, vol.37, issue.1, pp.73-93, 1993.
DOI : 10.4310/jdg/1214453423

H. Nicolaas and . Kuiper, On C 1 -isometric imbeddings. I, II. Nederl. Akad. Wetensch, Proc. Ser. A. 58 = Indag, pp.545-556, 1955.

P. Li and S. Yau, A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces, Inventiones Mathematicae, vol.7, issue.2, pp.269-291, 1982.
DOI : 10.1007/BF01399507

P. Mattila, Geometry of sets and measures in Euclidean spaces, volume 44 of Cambridge Studies in Advanced Mathematics, Fractals and rectifiability, 1995.

J. Milnor, On the Betti numbers of real varieties, Proc. Amer, pp.275-280, 1964.
DOI : 10.1090/S0002-9939-1964-0161339-9

N. Nadirashvili, Berger's isoperimetric problem and minimal immersions of surfaces, Geometric and Functional Analysis, vol.7, issue.5, pp.877-897, 1996.
DOI : 10.1007/BF02246788

J. Nash, The Imbedding Problem for Riemannian Manifolds, The Annals of Mathematics, vol.63, issue.1, pp.20-63, 1956.
DOI : 10.2307/1969989

L. Polterovich, Symplectic aspects of the first eigenvalue, Journal f??r die reine und angewandte Mathematik (Crelles Journal), vol.1998, issue.502, pp.1-17, 1998.
DOI : 10.1515/crll.1998.089

G. Pólya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics, Annals of Mathematics Studies, issue.27, 1951.

C. Robert and . Reilly, On the first eigenvalue of the Laplacian for compact submanifolds of Euclidean space, Comment. Math. Helv, vol.52, issue.4, pp.525-533, 1977.

C. Paul, S. Yang, and . Yau, Eigenvalues of the Laplacian of compact Riemann surfaces and minimal submanifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.7, issue.41, pp.55-63, 1980.