.. Perturbation, 108 2.8.1 Choice of the transverse vector field 108 2.8.2 Function spaces, 109 2.8.3 Mean curvature of the approximate solutions, p.114

.. Linear, 118 2.9.1 Linear analysis on the punctured disk 119 2.9.2 Linear analysis on the half-catenoid Linear analysis on the catenoid, p.132

.. Linear, 176 3.6.1 Linear analysis on a punctured CMC sphere, Gluing the parametrices together . . . . . . . . . . . . . . . . . . . . . . 182

U. Abresch and H. Rosenberg, A Hopf differential for constant mean curvature surfaces in S2??R and H2??R, Acta Mathematica, vol.193, issue.2, pp.141-174, 2004.
DOI : 10.1007/BF02392562

U. Abresch and H. Rosenberg, Generalized Hopf Differentials, Math. Contemp, vol.28, pp.1-28, 2005.

A. D. Alexandrov, Uniqueness theorems for surfaces in the large, Vestnik Leningrad Univ. Mat. Mekh. Astronom, p.13, 1958.

F. Almgren, Optimal isoperimetric inequalities, Bulletin of the American Mathematical Society, vol.13, issue.2, pp.123-126, 1985.
DOI : 10.1090/S0273-0979-1985-15393-5

F. Almgren, Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints, Memoirs of the American Mathematical Society, vol.4, issue.165, 1976.
DOI : 10.1090/memo/0165

C. Bavard and P. Pansu, Sur le volume minimal de R 2 Annales scientifiques de l' ´ Ecole Normale Supérieure, pp.479-490, 1986.

S. N. Bernstein, ???ber ein geometrisches Theorem und seine Anwendung auf die partiellen Differentialgleichungen vom elliptischen Typus, Mathematische Zeitschrift, vol.26, issue.1, pp.551-558, 1927.
DOI : 10.1007/BF01475472

P. Berard and D. Meyer, Inégalities isopériméetriques et applications, Ann. Sci. ´ Ec. Norm

A. I. Bobenko, All constant mean curvature tori inR 3,S 3,H 3 in terms of theta-functions, Mathematische Annalen, vol.121, issue.3, pp.209-245, 1991.
DOI : 10.1007/BF01459243

A. Butscher and R. Mazzeo, Constant mean curvature hypersurfaces condensing to geodesic segments and rays in riemannian manifolds, Ann. Sc. Norm. Super. Pisa Cl

A. Butscher and F. Pacard, Doubling constant mean curvature tori in S 3, pp.611-638, 2006.

P. Collin, Topology and curvature of properly embedded minimal surfaces in R 3, Annals of Math, issue.2 1, p.145, 1997.

P. Collin and H. Rosenberg, Construction of harmonic diffeomorphisms and minimal graphs, Annals of Mathematics, vol.172, issue.3, 2007.
DOI : 10.4007/annals.2010.172.1879

URL : https://hal.archives-ouvertes.fr/hal-00125426

C. J. Costa, Example of a complete minimal immersion in IR3 of genus one and three-embedded ends, Boletim da Sociedade Brasileira de Matem??tica, vol.22, issue.1-2, pp.47-54, 1984.
DOI : 10.1007/BF02584707

C. J. Costa, Uniqueness of minimal surfaces embedded in $\mathbf{R}^3,$ with total curvature $12\pi$, Journal of Differential Geometry, vol.30, issue.3, pp.597-618, 1989.
DOI : 10.4310/jdg/1214443825

C. J. Costa, Classification of complete minimal surfaces inR 3 with total curvature 12?, Inventiones Mathematicae, vol.21, issue.1, pp.273-303, 1991.
DOI : 10.1007/BF01232268

B. Daniel, Minimal disks bounded by three straight lines in Euclidean space and trinoids in hyperbolic space, Journal of Differential Geometry, vol.72, issue.3, pp.467-508, 2006.
DOI : 10.4310/jdg/1143593747

B. Daniel, Isometric immersions into 3-dimensional homogeneous manifolds, Commentarii Mathematici Helvetici, vol.82, issue.1, pp.87-131, 2007.
DOI : 10.4171/CMH/86

B. Daniel, Isometric immersions into $\mathbb {S}^n\times \mathbb {R}$ and $\mathbb {H}^n\times \mathbb {R}$ and applications to minimal surfaces, Transactions of the American Mathematical Society, vol.361, issue.12, pp.6255-6282, 2009.
DOI : 10.1090/S0002-9947-09-04555-3

B. Daniel and L. Hauswirth, Half-space theorem, embedded minimal annuli and minimal graphs in the Heisenberg group, Proc. London Math. Soc(3) 98, pp.445-470, 2009.
DOI : 10.1112/plms/pdn038

URL : https://hal.archives-ouvertes.fr/hal-00693132

B. Daniel and P. Mira, Existence and uniqueness of constant mean curvature spheres in Sol(3), American Journal of MathematicsVolume, vol.135, issue.3, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01097503

C. Delaunay, Sur la surface de révolution, dont la courbure moyenne est constante, Journal de mathématiques, vol.6, pp.309-320, 1841.

U. Dierkes, S. Hildebrandt, and H. Lewy, On the analyticity of minimal surfaces at movable boundaries of prescribed length, J. Reine Angew. Math, vol.379, pp.100-114, 1987.
DOI : 10.1007/978-1-4612-2082-4_40

S. Donaldson, Connections, cohomology and the intersection forms of 4-manifolds, Journal of Differential Geometry, vol.24, issue.3, pp.275-341, 1986.
DOI : 10.4310/jdg/1214440551

J. Dorfmeister, F. Pedit, and H. Wu, Weierstrass type representation of harmonic maps into symmetric spaces, Communications in Analysis and Geometry, vol.6, issue.4, pp.633-668, 1998.
DOI : 10.4310/CAG.1998.v6.n4.a1

J. Douglas, Solution of the problem of Plateau, Transactions of the American Mathematical Society, vol.33, issue.1, pp.263-321, 1931.
DOI : 10.1090/S0002-9947-1931-1501590-9

O. Druet, Sharp local isoperimetric inequalities involving the scalar curvature, Proceedings of the American Mathematical Society, pp.2351-2361, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00194440

A. Enneper, Analytisch-geometrische Untersuchungen, Z. Math. und Phys, vol.9, pp.96-125

M. Espinar and H. Rosenberg, Complete constant mean curvature surfaces in homogeneous spaces, Commentarii Mathematici Helvetici, vol.86, issue.3, pp.659-674, 2011.
DOI : 10.4171/CMH/237

L. Euler, Methodus inveniendi lineas curvas maximi minimive propietate gaudeates sive solutio problematis isoperimetrici latissimo sensu accepti A source book in mathematics, Opera, vol.1, issue.24, 1952.

I. Fernández and P. Mira, Harmonic maps and constant mean curvature surfaces in H 2 x R, American Journal of Mathematics, vol.129, issue.4, pp.1145-1181, 2007.
DOI : 10.1353/ajm.2007.0023

I. Fernández and P. Mira, Holomorphic quadratic differentials and the Bernstein problem in Heisenberg space. Transactions of the, pp.5737-5752, 2009.

A. Fraser and M. Li, Compactness of the space of embedded minimal surfaces with free boundary in three-manifolds with nonnegative Ricci curvature and convex boundary, Journal of Differential Geometry, vol.96, issue.2, pp.183-200, 2014.
DOI : 10.4310/jdg/1393424916

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

A. Fraser and R. Schoen, Sharp eigenvalue bounds and minimal surfaces in the ball, Inventiones mathematicae, vol.3, issue.5
DOI : 10.1007/s00222-015-0604-x

S. Gallot, Inégalités isopérimétriques et analytiques sur les variétés riemanniennes, Astérisque, vol.163, issue.164, pp.31-91, 1988.

D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, 2015.

K. Große-brauckmann, New surfaces of constant mean curvature, Mathematische Zeitschrift, vol.88, issue.1, pp.527-565, 1993.
DOI : 10.1007/BF02572424

M. Grüter, Boundary regularity for solutions of a partitioning problem Archive for Rational Mechanics and Analysis, pp.261-270, 1987.

L. Hauswirth, Minimal surfaces of Riemann type in three-dimensional product manifolds, Pacific Journal of Mathematics, vol.224, issue.1, pp.91-117, 2006.
DOI : 10.2140/pjm.2006.224.91

URL : https://hal.archives-ouvertes.fr/hal-00796841

L. Hauswrith and H. Rosenberg, Minimal surfaces of finite total curvature in H 2 × R, pp.65-80, 2006.

W. T. Hsiang and W. Y. Hsiang, On the uniqueness of isoperimetric solutions and imbedded soap bubbles in non-compact symmetric spaces, I, Inventiones Mathematicae, vol.121, issue.1, pp.39-58, 1989.
DOI : 10.1007/BF01388843

D. Hoffman and H. Karcher, Complete embedded minimal surfaces of finite total curvature, Geometry, V Encyclopaedia Math. Sci, vol.90, pp.5-93, 1997.

D. Hoffman, H. Karcher, and F. S. Wei, Adding Handles to the Helicoid, Bulletin of the American Mathematical Society, vol.29, issue.1, pp.77-84, 1993.
DOI : 10.1090/S0273-0979-1993-00401-4

D. Hoffman, H. Karcher, and F. S. Wei, The genus one helicoid and the minimal surfaces that led to its discovery. Global analysis in modern mathematics, 1991.

D. Hoffman and W. H. Meeks, A complete embedded minimal surface in ${\bf R}\sp 3$ with genus one and three ends, Journal of Differential Geometry, vol.21, issue.1, pp.109-127, 1985.
DOI : 10.4310/jdg/1214439467

D. Hoffman and W. H. Meeks, Embedded Minimal Surfaces of Finite Topology, The Annals of Mathematics, vol.131, issue.1, pp.1-34, 1990.
DOI : 10.2307/1971506

D. Hoffman and W. H. Meeks, Limits of minimal surfaces and Scherk's Fifth Surface Archive for Rational Mechanics and Analysis, pp.181-195, 1990.

D. Hoffman, M. Traizet, and B. White, Helicoidal minimal surfaces of prescribed genus. I. arXiv preprint
URL : https://hal.archives-ouvertes.fr/hal-01270167

M. Weber, D. Hoffman, and M. Wolf, An embedded genus-one helicoid, Proceedings of the National Academy of Sciences, vol.102, issue.46, pp.347-448, 2009.
DOI : 10.1073/pnas.0508008102

H. Hopf, Lectures on differential geometry in the large, 1956.

W. Y. Hsiang, Generalized rotational hypersurfaces of constant mean curvature in the Euclidean spaces. I, Journal of Differential Geometry, vol.17, issue.2, pp.337-356, 1982.
DOI : 10.4310/jdg/1214436924

W. Y. Hsiang, A symmetry theorem on isoperimetric regions, 1988.

J. H. Jellet, Sur la Surface dont la Courbure Moyenne est Constant, J. Math. Pures Appl, vol.18, pp.163-167, 1853.

N. Kapouleas, Complete Constant Mean Curvature Surfaces in Euclidean Three-Space, The Annals of Mathematics, vol.131, issue.2, pp.239-330, 1990.
DOI : 10.2307/1971494

N. Kapouleas, Constant mean curvature surfaces in Euclidean three-space, Proceedings of the International Congress of Mathematicians, pp.481-490, 1994.
DOI : 10.1090/S0273-0979-1987-15575-3

N. Kapouleas, Constant mean curvature surfaces constructed by fusing Wente tori, Inventiones Mathematicae, vol.121, issue.2, pp.443-518, 1995.
DOI : 10.1007/BF01245190

N. Kapouleas, Minimal surfaces in the round three-sphere by doubling the equatorial two-sphere. (2014) I. arXiv preprint

N. Kapouleas, Slowly rotating drops , Communications in mathematical physics, 1990.

N. Kapouleas and S. D. Yang, Minimal surfaces in the three-sphere by doubling the Clifford torus, American Journal of Mathematics, vol.132, issue.2, pp.257-295, 2010.
DOI : 10.1353/ajm.0.0104

H. Karcher, The triply periodic minimal surfaces of Alan Schoen and their constant mean curvature companions, Manuscripta Mathematica, vol.76, issue.3, pp.291-357, 1989.
DOI : 10.1007/BF01165824

N. Korevaar, R. Kusner, and B. Solomon, The structure of complete embedded surfaces with constant mean curvature, Journal of Differential Geometry, vol.30, issue.2, pp.465-503, 1989.
DOI : 10.4310/jdg/1214443598

R. Kusner, R. Mazzeo, and D. Pollack, The moduli space of complete embedded constant mean curvature surfaces. Geometric and Functional Analysis GAFA, pp.120-137, 1996.

O. A. Ladyzhenskaya and N. N. , Ural'ceva Equations aux dérivées partielles de type elliptique, 1968.

H. B. Lawson, Lectures on minimal submanifolds, 1980.

H. B. Lawson, Complete Minimal Surfaces in S 3, The Annals of Mathematics, vol.92, issue.3, pp.92-335, 1970.
DOI : 10.2307/1970625

H. Liebmann, Ueber die Verbiegung der geschlossenen Fl???chen positiver Kr???mmung, Mathematische Annalen, vol.18, issue.1-2, pp.81-112, 1900.
DOI : 10.1007/BF01456030

F. J. López and A. Ros, On embedded complete minimal surfaces of genus zero, Journal of Differential Geometry, vol.33, issue.1, pp.293-300, 1991.
DOI : 10.4310/jdg/1214446040

F. Mahmoudi, R. Mazzeo, and F. Pacard, Constant mean curvature hypersurfaces condensing on a submanifold, GAFA Geometric And Functional Analysis, vol.16, issue.4, pp.924-958, 2006.
DOI : 10.1007/s00039-006-0566-7

R. Mazzeo, Recent advances in the global theory of constant mean curvature surfaces, Contemp. Math, vol.350, pp.179-199, 2004.
DOI : 10.1090/conm/350/06345

R. Mazzeo and F. Pacard, Constant mean curvature surfaces with Delaunay ends, Communications in Analysis and Geometry, vol.9, issue.1, pp.169-237, 2001.
DOI : 10.4310/CAG.2001.v9.n1.a6

URL : http://arxiv.org/abs/math/9807039

R. Mazzeo and F. Pacard, Bifurcating nodoids, Contemp. Math, vol.314, pp.169-186, 2002.
DOI : 10.1090/conm/314/05430

R. Mazzeo and F. Pacard, Foliations by constant mean curvature tubes, Communications in Analysis and Geometry, vol.13, issue.4, pp.633-670, 2005.
DOI : 10.4310/CAG.2005.v13.n4.a1

R. Mazzeo, F. Pacard, and D. Pollack, Connected sums of constant mean curvature surfaces in Euclidean 3 space, Journal f??r die reine und angewandte Mathematik (Crelles Journal), vol.2001, issue.536, pp.115-165, 2001.
DOI : 10.1515/crll.2001.054

W. H. Meeks, Geometric results in classical minimal surface theory, 2003.

W. H. Meeks, The topology and geometry of embedded surfaces of constant mean curvature, Journal of Differential Geometry, vol.27, issue.3, pp.539-552, 1988.
DOI : 10.4310/jdg/1214442008

W. H. Meeks, The classification of complete minimal surfaces in $\mathbf{R}^3$, Duke Mathematical Journal, vol.48, issue.3, pp.523-535, 1981.
DOI : 10.1215/S0012-7094-81-04829-8

W. H. Meeks and J. Pérez, A survey on classical minimal surface theory, 2012.
DOI : 10.1090/ulect/060

W. H. Meeks and H. Rosenberg, The uniqueness of the helicoid and the asymptotic geometry of properly embedded minimal surfaces with finite topology, Annals of Math, vol.161, issue.2, 2005.

W. H. Meeks, J. Perez, and A. , Properly embedded minimal planar domains with infinite topology are Riemann minimal examples, Current Developments in Mathematics, vol.2008, issue.1, pp.281-346, 2009.
DOI : 10.4310/CDM.2008.v2008.n1.a4

W. H. Meeks, L. Simon, and S. T. Yau, Embedded minimal surfaces, exotic spheres and manifolds with positive Ricci curvature, Ann. of Math, issue.2, pp.116-621, 1982.

J. B. Meusnier, Mémoire sur la courbure des surfaces, Mém. Mathé m. Phys. Acad. Sci. Paris, prés. par div. Savans, vol.10, pp.477-510

F. Morgan, Regularity of isoperimetric hypersurfaces in Riemannian manifolds. Transactions of the, pp.5041-5052, 2003.

F. Morgan and I. Salavessa, The isoperimetric problem in higher codimension. arXiv preprint, 2012.

J. C. Nitsche, On the boundary regularity of surfaces of least area in euclidan spaces. Continuum Mechanics and related problems of analysis, pp.375-377, 1972.

S. Nardulli, The isoperimetric profile of a smooth Riemannian manifold for small volumes, Annals of Global Analysis and Geometry, vol.147, issue.2, pp.111-131, 2009.
DOI : 10.1007/s10455-008-9152-6

R. Osserman, A survey on Minimal Surfaces, 1986.

]. F. Pacard, Attaching handles to Delaunay nodoids, Pacific Journal of Mathematics, vol.266, issue.1, pp.129-183, 2013.
DOI : 10.2140/pjm.2013.266.129

URL : https://hal.archives-ouvertes.fr/hal-00851588

F. Pacard and T. Sun, Doubling constructions for constant mean curvature surfaces in Riemannian manifolds

F. Pacard and X. Xu, Constant mean curvature spheres in Riemannian manifolds, manuscripta mathematica, vol.147, issue.2, pp.275-295, 2009.
DOI : 10.1007/s00229-008-0230-7

P. Pansu, Sur la r??gularit?? du profil isop??rim??trique des surfaces riemanniennes compactes, Annales de l'institut Fourier, pp.247-264, 1998.
DOI : 10.5802/aif.1617

U. Pinkall and I. Sterling, On the Classification of Constant Mean Curvature Tori, The Annals of Mathematics, vol.130, issue.2, pp.407-451, 1989.
DOI : 10.2307/1971425

T. Radó, On Plateau's Problem, The Annals of Mathematics, vol.31, issue.3, pp.31-457, 1930.
DOI : 10.2307/1968237

J. Ratzkin, An end-to-end gluing construction for surfaces of constant mean curvature. (Doctoral dissertation, 2001.

M. Ritoré, Examples of constant mean curvature surfaces obtained from harmonic maps to the two sphere, Mathematische Zeitschrift, vol.226, issue.1, pp.127-146, 1997.
DOI : 10.1007/PL00004326

H. Rosenberg, Constant mean curvature surfaces in homogeneously regular 3-manifolds, Bulletin of the Australian Mathematical Society, vol.74, issue.02, pp.227-238, 2006.
DOI : 10.1007/BF00147301

J. Sacks and K. Uhlenbeck, The Existence of Minimal Immersions of 2-Spheres, The Annals of Mathematics, vol.113, issue.1, pp.1-24, 1981.
DOI : 10.2307/1971131

H. F. Scherk, BemerkungenüberBemerkungen¨Bemerkungenüber die kleinste Fläache innerhalb gegebener Grenzen, J. R. Angew. Math, vol.13, pp.185-208
DOI : 10.1515/crll.1835.13.185

URL : http://www.digizeitschriften.de/download/PPN243919689_0013/PPN243919689_0013___log15.pdf

R. Schoen, The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation, Communications on Pure and Applied Mathematics, vol.19, issue.3, pp.317-392, 1988.
DOI : 10.1002/cpa.3160410305

R. Schoen, Uniqueness, symmetry, and embeddedness of minimal surfaces, Journal of Differential Geometry, vol.18, issue.4, pp.791-809, 1983.
DOI : 10.4310/jdg/1214438183

R. Schoen and S. T. Yau, Existence of incompressible minimal surfaces and the topology of 3-dimensional manifolds with nonnegative scalar curvature, Ann. of Math, issue.2, pp.110-127, 1979.

M. Schneider, Closed magnetic geodesics on $S^2$, Journal of Differential Geometry, vol.87, issue.2, pp.343-388, 2011.
DOI : 10.4310/jdg/1304514976

H. A. Schwarz, Gesammelte Mathematische Abhandlungen, 1933.
DOI : 10.1007/978-3-642-50665-9

L. Simon, Entire solutions of the minimal surface equation, Journal of Differential Geometry, vol.30, issue.3, pp.643-688, 1989.
DOI : 10.4310/jdg/1214443827

T. Sun, A note on constant geodesic curvature curves on surfaces Annales de l'I.H.P. Analyse non linéaire, pp.1569-1584, 2009.

C. Taubes, Self-dual connections on 4-manifolds with indefinite intersection matrix, Journal of Differential Geometry, vol.19, issue.2, pp.517-560, 1984.
DOI : 10.4310/jdg/1214438690

H. C. Wente, Counterexample to a conjecture of H. Hopf, Pacific Journal of Mathematics, vol.121, issue.1, pp.193-242, 1986.
DOI : 10.2140/pjm.1986.121.193

R. Ye, Foliation by constant mean curvature spheres, Pacific Journal of Mathematics, vol.147, issue.2, pp.381-396, 1991.
DOI : 10.2140/pjm.1991.147.381