Test configuration and geodesic rays
Géométrie différentielle, physique mathématique, mathématiques et société (I) : Volume en l'honneur de Jean Pierre Bourguignon, Astérisque, no. 321 (2008), pp. 139-167.
@incollection{AST_2008__321__139_0,
     author = {Chen, Xiuxiong and Tang, Yudong},
     title = {Test configuration and geodesic rays},
     booktitle = {G\'eom\'etrie diff\'erentielle, physique math\'ematique, math\'ematiques et soci\'et\'e (I) : Volume en l'honneur de Jean Pierre Bourguignon},
     editor = {Hijazi Oussama},
     series = {Ast\'erisque},
     pages = {139--167},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {321},
     year = {2008},
     mrnumber = {2521647},
     zbl = {1181.53058},
     language = {en},
     url = {http://archive.numdam.org/item/AST_2008__321__139_0/}
}
TY  - CHAP
AU  - Chen, Xiuxiong
AU  - Tang, Yudong
TI  - Test configuration and geodesic rays
BT  - Géométrie différentielle, physique mathématique, mathématiques et société (I) : Volume en l'honneur de Jean Pierre Bourguignon
AU  - Collectif
ED  - Hijazi Oussama
T3  - Astérisque
PY  - 2008
SP  - 139
EP  - 167
IS  - 321
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/AST_2008__321__139_0/
LA  - en
ID  - AST_2008__321__139_0
ER  - 
%0 Book Section
%A Chen, Xiuxiong
%A Tang, Yudong
%T Test configuration and geodesic rays
%B Géométrie différentielle, physique mathématique, mathématiques et société (I) : Volume en l'honneur de Jean Pierre Bourguignon
%A Collectif
%E Hijazi Oussama
%S Astérisque
%D 2008
%P 139-167
%N 321
%I Société mathématique de France
%U http://archive.numdam.org/item/AST_2008__321__139_0/
%G en
%F AST_2008__321__139_0
Chen, Xiuxiong; Tang, Yudong. Test configuration and geodesic rays, dans Géométrie différentielle, physique mathématique, mathématiques et société (I) : Volume en l'honneur de Jean Pierre Bourguignon, Astérisque, no. 321 (2008), pp. 139-167. http://archive.numdam.org/item/AST_2008__321__139_0/

[1] M. Abreu - "Kähler geometry of toric varieties and extremal metrics", Internat. J. Math. 9 (1998), p. 641-651. | DOI | MR | Zbl

[2] V. Apostolov, D. M. J. Calderbank, P. Gauduchon & C. W. Tønnesen-Friedman - "Hamiltonian 2-forms in Kähler geometry. III. Extremal metrics and stability", Invent. Math. 173 (2008), p. 547-601. | DOI | MR | Zbl

[3] C. Arezzo & G. Tian - "Infinite geodesic rays in the space of Kähler potentials", Ann. Sc. Norm. Super. Pisa Cl. Sci. 2 (2003), p. 617-630. | EuDML | Numdam | MR | Zbl

[4] E. Bedford & B. A. Taylor - "The Dirichlet problem for a complex Monge-Ampère equation", Invent. Math. 37 (1976), p. 1-44. | DOI | EuDML | MR | Zbl

[5] E. Calabi - "Extremal Kähler metrics", in Seminar on Differential Geometry, Ann. of Math. Stud., vol. 102, Princeton Univ. Press, 1982, p. 259-290. | MR | Zbl

[6] E. Calabi, "Extremal Kähler metrics. II", in Differential geometry and complex analysis, Springer, 1985, p. 95-114. | DOI | MR | Zbl

[7] E. Calabi & X. Chen - "The space of Kähler metrics. II", J. Differential Geom. 61 (2002), p. 173-193. | DOI | MR | Zbl

[8] X. Chen - "The space of Kähler metrics", J. Differential Geom. 56 (2000), p. 189-234. | DOI | MR | Zbl

[9] X. Chen, "Space of Kähler metrics. III — On the lower bound of the Calabi energy and geodesic distance", Invent. math. (2008), DOI: 10.1007/s00222-008-0153-7. | MR | Zbl

[10] X. Chen & G. Tian - "Geometry of Kähler metrics and foliations by holomorphic discs", Publ. Math. Inst. Hautes Études Sci. 107 (2008), p. 1-107. | DOI | EuDML | Numdam | MR | Zbl

[11] W. Y. Ding & G. Tian - "Kähler-Einstein metrics and the generalized Futaki invariant", Invent. Math. 110 (1992), p. 315-335. | DOI | EuDML | MR | Zbl

[12] S. K. Donaldson - "Symmetric spaces, Kähler geometry and Hamiltonian dynamics", in Northern California Symplectic Geometry Seminar, Amer. Math. Soc. Transl. Ser. 2, vol. 196, Amer. Math. Soc., 1999, p. 13-33. | MR | Zbl

[13] S. K. Donaldson, "Scalar curvature and projective embeddings. I", J. Differential Geom. 59 (2001), p. 479-522. | DOI | MR | Zbl

[14] S. K. Donaldson, "Holomorphic discs and the complex Monge-Ampere equation", J. Symplectic Geom. 1 (2002), p. 171-196. | DOI | MR | Zbl

[15] S. K. Donaldson, "Scalar curvature and stability of toric varieties", J. Differential Geom. 62 (2002), p. 289-349. | DOI | MR | Zbl

[16] S. K. Donaldson, "Lower bounds on the Calabi functional", J. Differential Geom. 70 (2005), p. 453-472. | DOI | MR | Zbl

[17] A. Futaki - "An obstruction to the existence of Einstein Kähler metrics", Invent. Math. 73 (1983), p. 437-443. | DOI | EuDML | MR | Zbl

[18] B. Guan - "The Dirichlet problem for complex Monge-Ampere equations and regularity of the pluri-complex Green function", Comm. Anal. Geom. 6 (1998), p. 687-703. | DOI | MR | Zbl

[19] M. Levine - "A remark on extremal Kähler metrics", J. Differential Geom. 21 (1985), p. 73-77. | DOI | MR | Zbl

[20] Z. Lu & G. Tian - "The log term of the Szegö kernel", Duke Math. J. 125 (2004), p. 351-387. | DOI | MR | Zbl

[21] T. Mabuchi - "Some symplectic geometry on compact Kähler manifolds. I", Osaka J. Math. 24 (1987), p. 227-252. | MR | Zbl

[22] T. Mabuchi, "Stability of extremal Kähler manifolds", Osaka J. Math. 41 (2004), p. 563-582. | MR | Zbl

[23] S. T. Paul & G. Tian - "Analysis of geometric stability", Int. Math. Res. Not. 48 (2004), p. 2555-2591. | DOI | MR | Zbl

[24] D. H. Phong & J. Sturm - "Stability, energy functional, and Kähler-Einstein metrics", Comm. Anal. Geom. 11 (2003), p. 565-597. | DOI | MR | Zbl

[25] D. H. Phong & J. Sturm, "The Monge-Ampère operator and geodesies in the space of Kähler potentials", Invent. Math. 166 (2006), p. 125-149. | DOI | MR | Zbl

[26] D. H. Phong & J. Sturm, "Test configurations for K-stability and geodesic rays", J. Symplectic Geom. 5 (2007), p. 221-247. | DOI | MR | Zbl

[27] D. H. Phong & J. Sturm, "On the regularity of geodesic rays associated to test configurations", preprint arXiv:0707.3956.

[28] J. Ross & R. Thomas - "A study of the Hilbert-Mumford criterion for the stability of projective varieties", J. Algebraic Geom. 16 (2007), p. 201-255. | DOI | MR | Zbl

[29] S. Semmes - "Complex Monge-Ampère and symplectic manifolds", Amer. J. Math. 114 (1992), p. 495-550. | DOI | MR | Zbl

[30] S. Semmes, "The homogeneous complex Monge-Ampère equation and the infinite-dimensional versions of classic symmetric spaces", in The Gelfand Mathematical Seminars, 1993-1995, Gelfand Math. Sem., Birkhäuser, 1996, p. 225-242. | DOI | MR | Zbl

[31] J. Song & S. Zelditch - "Bergman metrics and geodesics in the space of Kähler metrics on toric varieties", preprint arXiv:0707.3082. | DOI | MR | Zbl

[32] G. Székelyhidi - "Extremal metrics and K-stability", Bull. Lond. Math. Soc. 39 (2007), p. 76-84. | DOI | MR | Zbl

[33] G. Tian - "On a set of polarized Kähler metrics on algebraic manifolds", J. Differential Geom. 32 (1990), p. 99-130. | DOI | MR | Zbl

[34] G. Tian, "Kähler-Einstein metrics with positive scalar curvature", Invent. Math. 130 (1997), p. 1-37. | DOI | MR | Zbl

[35] S. T. Yau - "On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation. I", Comm. Pure Appl. Math. 31 (1978), p. 339-411. | DOI | MR | Zbl

[36] S. Zelditch - "Szegő kernels and a theorem of Tian", Internat. Math. Res. Notices 6 (1998), p. 317-331. | DOI | MR | Zbl

[37] B. Zhou & X. H. Zhu - "A note on the K-stability on toric manifolds", preprint arXiv:0706.0505. | Zbl