L. V. Ahlfors, . Lectures-on-quasiconformal-mappings, &. Wadsworth, . J. Brooks, and J. Earle, With the assistance of C, 1987.

L. V. Ahlfors and L. Bers, Riemann's mapping theorem for variable metrics, Ann. of Math, issue.2, pp.72-385, 1960.

M. Alber, R. Camassa, Y. Fedorov, D. D. Holm, and J. E. Marsden, The Complex Geometry of Weak Piecewise Smooth Solutions of Integrable Nonlinear PDE's??of Shallow Water and Dym Type, Communications in Mathematical Physics, vol.221, issue.1, pp.221-197, 2001.
DOI : 10.1007/PL00005573

V. I. Arnold, Sur la g??om??trie diff??rentielle des groupes de Lie de dimension infinie et ses applications ?? l'hydrodynamique des fluides parfaits, Annales de l???institut Fourier, vol.16, issue.1, pp.319-361, 1966.
DOI : 10.5802/aif.233

A. Beurling and L. V. Ahlfors, The boundary correspondence under quasiconformal mappings, Acta Mathematica, vol.96, issue.0, pp.125-142, 1956.
DOI : 10.1007/BF02392360

J. Bourguignon and H. Brezis, Remarks on the Euler equation, Journal of Functional Analysis, vol.15, issue.4, pp.341-363, 1974.
DOI : 10.1016/0022-1236(74)90027-5

G. Buttazzo, M. Giaquinta, and S. Hildebrandt, One-Dimensional Variational Problems. An Introduction , Oxford Lecture Ser, Math. Appl, vol.15, 1998.

J. Chemin, Perfect Incompressible Fluids, Oxford Lecture Ser, Math. Appl, vol.14, 1998.

C. J. Earle, F. P. Gardiner, and N. Lakic, Asymptotic Teichm??ller space. I. The complex structure, Contemp. Math, vol.256, pp.17-38, 2000.
DOI : 10.1090/conm/256/03995

D. G. Ebin and J. E. Marsden, Groups of Diffeomorphisms and the Motion of an Incompressible Fluid, The Annals of Mathematics, vol.92, issue.1, pp.102-163, 1970.
DOI : 10.2307/1970699

F. P. Gardiner, Teichmüller Theory and Quadratic Differentials, Pure Appl, Math, 1987.

F. P. Gardiner and W. J. Harvey, Handbook of Complex Analysis: Geometric Function Theory, pp.457-492, 2002.

F. P. Gardiner and D. P. Sullivan, Symmetric Structures on a Closed Curve, American Journal of Mathematics, vol.114, issue.4, pp.683-736, 1992.
DOI : 10.2307/2374795

F. Gay-balmaz, Infinite dimensional geodesic flows and the universal Teichmüller space, 2008.

E. Hewitt and K. Stromberg, Real and abstract analysis, in: A Modern Treatment of the Theory of Functions of a Real Variable, third printing, Grad. Texts in Math, vol.25, 1975.

D. D. Holm and J. E. Marsden, Momentum maps and measure-valued solutions (peakons, filaments, and sheets) for the EPDiff equation, Progr. Math, vol.232, pp.203-235, 2004.
DOI : 10.1007/0-8176-4419-9_8

A. A. Kirillov, K???hler structures on K-orbits of the group of diffeomorphisms of a circle, Functional Analysis and Its Applications, vol.42, issue.2, pp.122-125, 1986.
DOI : 10.1007/BF01078025

A. W. Knapp, Basic Real Analysis, 2005.

A. Kriegl and P. W. Michor, The Convenient Setting of Global Analysis, Math. Surveys Monogr, vol.53, 1997.
DOI : 10.1090/surv/053

S. Kushnarev, Teichons: Solitonlike Geodesics on Universal Teichm??ller Space, Experimental Mathematics, vol.18, issue.3, pp.325-336, 2009.
DOI : 10.1080/10586458.2009.10129054

S. Lang, Fundamentals of Differential Geometry, Grad. Texts in Math, vol.191, 1999.
DOI : 10.1007/978-1-4612-0541-8

O. Lehto, Univalent Functions and Teichmüller Spaces, Grad. Texts in Math, vol.109, 1987.

J. E. Marsden, Well-posedness of the equations of a non-homogeneous perfect fluid, Communications in Partial Differential Equations, vol.20, issue.3, pp.215-230, 1976.
DOI : 10.1080/03605307608820010

J. E. Marsden, T. S. Ratiu, and S. Shkoller, The geometry and analysis of the averaged Euler equations and a new diffeomorphism group, Geometric and Functional Analysis, vol.10, issue.3, pp.582-599, 2000.
DOI : 10.1007/PL00001631

G. Misiolek, Stability of flows of ideal fluids and the geometry of the group of diffeomorphisms, Math. J, vol.2, pp.215-235, 1993.

S. Nag, The Complex Analytic Theory of Teichmüller Spaces, 1988.

S. Nag and A. Verjovsky, Diff (S 1) and the Teichm??ller spaces, Communications in Mathematical Physics, vol.26, issue.1, pp.123-138, 1990.
DOI : 10.1007/BF02099878

H. Omori, Infinite-Dimensional Lie Groups, Transl. Math. Monogr, vol.158, 1997.

R. S. Palais, Foundations of Global Non-linear Analysis, 1968.

M. Reimann, Ordinary differential equations and quasiconformal mappings, Inventiones Mathematicae, vol.36, issue.3, pp.247-270, 1976.
DOI : 10.1007/BF01404205
URL : http://www.digizeitschriften.de/download/PPN356556735_0033/PPN356556735_0033___log41.pdf

T. Runst and W. Sickel, Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations, De Gruyter Ser, Nonlinear Anal. Appl, vol.3, 1996.

E. Sharon and D. Mumford, 2D-Shape Analysis Using Conformal Mapping, International Journal of Computer Vision, vol.70, issue.1, pp.55-75, 2006.
DOI : 10.1007/s11263-006-6121-z
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.122.783

S. Shkoller, Analysis on Groups of Diffeomorphisms of Manifolds with Boundary and the Averaged Motion of a Fluid, Journal of Differential Geometry, vol.55, issue.1, pp.145-191, 2000.
DOI : 10.4310/jdg/1090340568

L. Takhtajan and L. Teo, Weil?Petersson metric on the universal Teichmüller space, Mem. Amer. Math. Soc, vol.183, issue.861, 2006.

L. Teo, The Velling-Kirillov metric on the universal Teichm??ller curve, Journal d'Analyse Math??matique, vol.33, issue.4, pp.271-307, 2004.
DOI : 10.1007/BF02789310

A. Trouvé, Diffeomorphic groups and pattern matching in image analysis, International Journal of Computer Vision, vol.28, issue.3, pp.213-221, 1998.
DOI : 10.1023/A:1008001603737

A. Trouvé and L. Younes, Local Geometry of Deformable Templates, SIAM Journal on Mathematical Analysis, vol.37, issue.1, pp.17-59, 2005.
DOI : 10.1137/S0036141002404838

L. Younes, Shapes and Diffeomorphisms, Appl. Math. Sci, vol.171, 2010.
DOI : 10.1007/978-3-642-12055-8