C. Arezzo, A. Ghigi, and A. Loi, Stable bundles and the first eigenvalue of the Laplacian, Journal of Geometric Analysis, vol.3, issue.2, pp.375-386, 2007.
DOI : 10.1007/BF02922088

D. Bakry and M. Émery, Diffusions hypercontractives, Séminaire de probabilités, pp.177-206, 1983.
DOI : 10.1007/BFb0075847

URL : http://archive.numdam.org/article/SPS_1985__19__177_0.pdf

P. H. Bérard, Spectral geometry: direct and inverse problems, of Monografías de Matemática [Mathematical Monographs]. Instituto de Matemática Pura e Aplicada (IMPA) With appendices by Gérard Besson, 1986.
DOI : 10.1007/BFb0076330

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

R. Brooks and E. Makover, Riemann surfaces with large first eigenvalue, Journal d'Analyse Math??matique, vol.84, issue.1, pp.243-258, 2001.
DOI : 10.1007/BF02790263

P. Buser, A note on the isoperimetric constant, Annales scientifiques de l'??cole normale sup??rieure, vol.15, issue.2, pp.213-230, 1982.
DOI : 10.24033/asens.1426

M. Chaperon and D. Meyer, On a theorem of Ren?? Thom in G??om??trie Finie, L???Enseignement Math??matique, vol.55, issue.3, pp.55-58, 2009.
DOI : 10.4171/LEM/55-3-6

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

Q. Cheng and H. Yang, Inequalities for eigenvalues of Laplacian on domains and compact complex hypersurfaces in complex projective spaces, Journal of the Mathematical Society of Japan, vol.58, issue.2, pp.545-561, 2006.
DOI : 10.2969/jmsj/1149166788

S. Y. Cheng, Eigenvalue comparison theorems and its geometric applications, Mathematische Zeitschrift, vol.9, issue.3, pp.289-297, 1975.
DOI : 10.1007/BF01214381

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

B. Colbois, E. Dryden, and A. Soufi, Bounding the eigenvalues of the Laplace-Beltrami operator on compact submanifolds, Bulletin of the London Mathematical Society, vol.42, issue.1, pp.96-108, 2010.
DOI : 10.1112/blms/bdp100

URL : https://hal.archives-ouvertes.fr/hal-00420689

B. Colbois and A. 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, A. Soufi, and A. Girouard, Isoperimetric control of the Steklov spectrum, Journal of Functional Analysis, vol.261, issue.5, pp.1384-1399, 2011.
DOI : 10.1016/j.jfa.2011.05.006

URL : https://hal.archives-ouvertes.fr/hal-00779282

B. Colbois, A. Soufi, and A. Girouard, Isoperimetric control of the spectrum of a compact hypersurface, 2012

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, I. Evans, M. 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

A. Soufi and S. Ilias, Majoration de la seconde valeur propre d'un op??rateur de Schr??dinger sur une vari??t?? compacte et applications, Journal of Functional Analysis, vol.103, issue.2, pp.294-316, 1992.
DOI : 10.1016/0022-1236(92)90123-Z

A. Fraser and R. Schoen, The first Steklov eigenvalue, conformal geometry, and minimal surfaces, Advances in Mathematics, vol.226, issue.5, pp.4011-4030, 2011.
DOI : 10.1016/j.aim.2010.11.007

L. Friedlander and N. Nadirashvili, A differential invariant related to the first eigenvalue of the Laplacian, Internat. Math. Res. Notices, issue.17, pp.939-952, 1999.

A. Girouard and I. Polterovich, Shape optimization for low Neumann and Steklov eigenvalues, Mathematical Methods in the Applied Sciences, vol.102, issue.2, pp.501-516, 2010.
DOI : 10.1002/mma.1222

URL : https://hal.archives-ouvertes.fr/hal-00576288

A. Girouard and I. Polterovich, Upper bounds for Steklov eigenvalues on surfaces, Electronic Research Announcements in Mathematical Sciences, vol.19, issue.0, 2012.
DOI : 10.3934/era.2012.19.77

P. Griffiths and J. Harris, Principles of algebraic geometry, 1978.
DOI : 10.1002/9781118032527

A. Grigor-'yan, Y. Netrusov, and Y. Yau, Eigenvalues of elliptic operators and geometric applications. Surveys in Diff, pp.147-217, 2004.

A. Grigor-'yan and S. Yau, Decomposition of a metric space by capacitors, Differential equations, pp.39-75, 1996.

M. Gromov, Metric invariants of Kähler manifolds, Differential geometry and topology, pp.90-116, 1992.

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

P. Li, S. Yau, P. Li, and S. Yau, Estimates of eigenvalues of a compact Riemannian manifold A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces, Geometry of the Laplace operator (Proc. Sympos. Pure Math., Univ. Hawaii, Honolulu, Hawaii Proc. Sympos. Pure Math., XXXVI, pp.205-239269, 1979.

J. Lohkamp, Discontinuity of geometric expansions, Commentarii Mathematici Helvetici, vol.71, issue.1, pp.213-228, 1996.
DOI : 10.1007/BF02566417

J. Lott and C. Villani, Ricci curvature for metric-measure spaces via optimal transport, Annals of Mathematics, vol.169, issue.3, pp.903-991, 2009.
DOI : 10.4007/annals.2009.169.903

URL : http://arxiv.org/abs/math/0412127

Z. Lu and J. Rowlett, Eigenvalues of collapsing domains and drift Laplacians, Mathematical Research Letters, vol.19, issue.3, pp.10001-100, 2010.
DOI : 10.4310/MRL.2012.v19.n3.a10

O. Munteanu and J. Wang, Analysis of weighted Laplacian and applications to Ricci solitons, Communications in Analysis and Geometry, vol.20, issue.1
DOI : 10.4310/CAG.2012.v20.n1.a3

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.

A. G. Setti, Eigenvalue estimates for the weighted Laplacian on a Riemannian manifold, Rend. Sem. Mat. Univ. Padova, vol.100, pp.27-55, 1998.

Y. Su and H. Zhang, Rigidity of manifolds with Bakry?????mery Ricci curvature bounded below, Geometriae Dedicata, vol.361, issue.1
DOI : 10.1007/s10711-011-9685-x

M. Taylor, Partial differential equations. II, Applied Mathematical Sciences, vol.116, 1996.

H. Urakawa, On the least positive eigenvalue of the Laplacian for compact group manifolds, Journal of the Mathematical Society of Japan, vol.31, issue.1, pp.209-226, 1979.
DOI : 10.2969/jmsj/03110209

G. Wei and W. Wylie, Comparison geometry for the Bakry-Emery Ricci tensor, Journal of Differential Geometry, vol.83, issue.2, pp.377-405, 2009.
DOI : 10.4310/jdg/1261495336

J. Wu, Upper bounds on the first eigenvalue for a diffusion operator via Bakry?????mery Ricci curvature, Journal of Mathematical Analysis and Applications, vol.361, issue.1, pp.10-18, 2010.
DOI : 10.1016/j.jmaa.2009.09.019

J. Wu, Upper Bounds on the First Eigenvalue for a Diffusion Operator via Bakry?????mery Ricci Curvature II, Results in Mathematics, vol.28, issue.3-4, 2011.
DOI : 10.1007/s00025-012-0254-x

P. C. Yang and S. 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.

S. Yau, SURVEY ON PARTIAL DIFFERENTIAL EQUATIONS IN 3 DIFFERENTIAL GEOMETRY, Seminar on Differential Geometry, pp.3-71, 1982.
DOI : 10.1515/9781400881918-002