V. Apostolov, D. M. Calderbank, P. Gauduchon, and C. Tønnesen-friedman, Hamiltonian 2-forms in K??hler geometry, II Global Classification, Journal of Differential Geometry, vol.68, issue.2, pp.277-345, 2004.
DOI : 10.4310/jdg/1115669513

O. Biquard and Y. Rollin, Smoothing singular constant scalar curvature K??hler surfaces and minimal Lagrangians, Advances in Mathematics, vol.285, pp.980-1024, 2015.
DOI : 10.1016/j.aim.2015.08.013

T. Delzant, Hamiltoniens p??riodiques et images convexes de l'application moment, Bulletin de la Société mathématique de France, vol.116, issue.3, pp.315-339, 1988.
DOI : 10.24033/bsmf.2100

P. Gauduchon, An introduction to Kähler geometry

V. Guillemin, Kaehler structures on toric varieties, Journal of Differential Geometry, vol.40, issue.2, pp.285-309, 1994.
DOI : 10.4310/jdg/1214455538

D. Joyce, Y. Lee, and R. Schoen, On the existence of Hamiltonian stationary Lagrangian submanifolds in symplectic manifolds, American Journal of Mathematics, vol.133, issue.4, pp.1067-1092, 2011.
DOI : 10.1353/ajm.2011.0030

Y. Lee, The existence of Hamiltonian stationary Lagrangian tori in K??hler manifolds of any dimension, Calculus of Variations and Partial Differential Equations, vol.147, issue.2, pp.231-251, 2012.
DOI : 10.1007/s00526-011-0457-0

E. Lerman and S. Tolman, Hamiltonian torus actions on symplectic orbifolds and toric varieties, Transactions of the American Mathematical Society, vol.349, issue.10, pp.4201-4230, 1997.
DOI : 10.1090/S0002-9947-97-01821-7

Y. Oh, Second variation and stabilities of minimal lagrangian submanifolds in K???hler manifolds, Inventiones Mathematicae, vol.2, issue.1, pp.501-519, 1990.
DOI : 10.1007/BF01231513

Y. Oh, Volume minimization of Lagrangian submanifolds under Hamiltonian deformations, Mathematische Zeitschrift, vol.36, issue.1, pp.175-192, 1993.
DOI : 10.1007/BF02571651

H. Ono, Hamiltonian stability of Lagrangian tori in toric K??hler manifolds, Annals of Global Analysis and Geometry, vol.212, issue.10, pp.329-343, 2007.
DOI : 10.1007/s10455-006-9037-5

R. Schoen and J. Wolfson, Minimizing volume among Lagrangian submanifolds, Differential equations of Proc. Sympos. Pure Math, pp.181-199, 1996.
DOI : 10.1090/pspum/065/1662755

R. Schoen and J. Wolfson, Minimizing Area Among Lagrangian Surfaces: The Mapping Problem, Journal of Differential Geometry, vol.58, issue.1, pp.1-86, 2001.
DOI : 10.4310/jdg/1090348282

E. Legendre, 118 route de Narbonne, 31062 Toulouse, France E-mail address: eveline.legendre@math.univ-toulouse