New results and problems on Kähler-Ricci flow
Géométrie différentielle, physique mathématique, mathématiques et société (II) - Volume en l'honneur de Jean-Pierre Bourguignon, Astérisque, no. 322 (2008), pp. 71-92.
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     author = {Tian, Gang},
     title = {New results and problems on {K\"ahler-Ricci} flow},
     booktitle = {G\'eom\'etrie diff\'erentielle, physique math\'ematique, math\'ematiques et soci\'et\'e (II) - Volume en l'honneur de Jean-Pierre Bourguignon},
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     pages = {71--92},
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     number = {322},
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Tian, Gang. New results and problems on Kähler-Ricci flow, dans Géométrie différentielle, physique mathématique, mathématiques et société (II) - Volume en l'honneur de Jean-Pierre Bourguignon, Astérisque, no. 322 (2008), pp. 71-92. http://archive.numdam.org/item/AST_2008__322__71_0/

[1] H. D. Cao - "Deformation of Kähler metrics to Kähler-Einstein metrics on compact Kähler manifolds", Invent. Math. 81 (1985), p. 359-372. | DOI | EuDML | MR | Zbl

[2] P. Cascini & G. La Nave - "Kähler-Ricci flow and the minimal model program for projective varieties", preprint arXiv:math.DG/0603064.

[3] X. Chen, P. Lu & G. Tian - "A note on uniformization of Riemann surfaces by Ricci flow", Proc. Amer. Math. Soc. 134 (2006), p. 3391-3393. | DOI | MR | Zbl

[4] X. Chen & G. Tian - "Ricci flow on Kähler-Einstein surfaces", Invent. Math. 147 (2002), p. 487-544. | DOI | MR | Zbl

[5] X. Chen & G. Tian, "Ricci flow on Kähler-Einstein manifolds", Duke Math. J. 131 (2006), p. 17-73. | DOI | MR | Zbl

[6] X. Chen, G. Tian & Z. Zhang - "On the weak Kähler-Ricci flow", preprint arXiv:0802.0809. | MR | Zbl

[7] B. Chow - "The Ricci flow on the 2-sphere", J. Differential Geom. 33 (1991), p. 325-334. | DOI | MR | Zbl

[8] J. Demailly & N. Pali - "Degenerate complex Monge-Ampère equations over compact Kähler manifolds", preprint arXiv:0710.5109. | DOI | MR | Zbl

[9] S. Dinew & Z. Zhang - "Stability of bounded solutions for degenerate complex Monge-Ampère equations", preprint arXiv:0711.3643.

[10] L. C. Evans - "Classical solutions of fully nonlinear, convex, second-order elliptic equations", Comm. Pure Appl. Math. 35 (1982), p. 333-363. | DOI | MR | Zbl

[11] P. Eyssidieux, V. Guedj & A. Zeriahi - "A priori L -estimates for degenerate complex Monge-Ampère equations", preprint arXiv:0712.3743. | MR | Zbl

[12] D. Gilbarg & N. S. Trudinger - Elliptic partial differential equations of second order, second ed., Grund. Math. Wiss., vol. 224, Springer, 1983. | MR | Zbl

[13] R. S. Hamilton - "The Ricci flow on surfaces", in Mathematics and general relativity (Santa Cruz, CA, 1986), Contemp. Math., vol. 71, Amer. Math. Soc., 1988, p. 237-262. | DOI | MR | Zbl

[14] R. S. Hamilton, "The formation of singularities in the Ricci flow", in Surveys in differential geometry, Vol II (Cambridge, MA, 1993), Int. Press, Cambridge, MA, 1995, p. 7-136. | MR | Zbl

[15] Y. Kawamata - "The cone of curves of algebraic varieties", Ann. of Math. 119 (1984), p. 603-633. | DOI | MR | Zbl

[16] Y. Kawamata, "Pluricanonical systems on minimal algebraic varieties", Invent. Math. 79 (1985), p. 567-588. | DOI | EuDML | MR | Zbl

[17] S. Kolodziej - "The complex Monge-Ampère equation", Acta Math. 180 (1998), p. 69-117. | DOI | MR | Zbl

[18] G. Perelman - "The entropy formula for the Ricci flow and its geometric applications", preprint arXiv:math.DG/0211159. | Zbl

[19] N. Sesum & G. Tian - "Perelman's argument for uniform bounded scalar curvature and diameter along the Kähler-Ricci flow", 2005, preprint.

[20] J. Song & G. Tian - "The Kähler-Ricci flow on surfaces of positive Kodaira dimension", Invent. Math. 170 (2007), p. 609-653. | DOI | MR | Zbl

[21] J. Song & G. Tian, in preparation.

[22] J. Song & G. Tian, "Canonical measures and Kähler-Ricci flow", preprint arXiv:0802.2570. | DOI | MR | Zbl

[23] G. Tian - "On Kähler-Einstein metrics on certain Kähler manifolds with C 1 (M)>0", Invent. Math. 89 (1987), p. 225-246. | DOI | EuDML | MR | Zbl

[24] G. Tian, "Smoothness of the universal deformation space of compact Calabi-Yau manifolds and its Petersson-Weil metric", in Mathematical aspects of string theory (San Diego, Calif, 1986), Adv. Ser. Math. Phys., vol. 1, World Sci. Publishing, 1987, p. 629-646. | DOI | MR | Zbl

[25] G. Tian, "On the existence of solutions of a class of Monge-Ampère equations", Acta Math. Sinica (N.S.) 4 (1988), p. 250-265. | DOI | MR | Zbl

[26] G. Tian, "On Calabi's conjecture for complex surfaces with positive first Chern class", Invent. Math. 101 (1990), p. 101-172. | DOI | EuDML | MR | Zbl

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

[28] G. Tian, "Geometry and nonlinear analysis", in Proceedings of the International Congress of Mathematicians, Vol. I (Beijing, 2002), Higher Ed. Press, 2002, p. 475-493. | MR | Zbl

[29] G. Tian & J. Viaclovsky - "Moduli spaces of critical Riemannian metrics in dimension four", Adv. Math. 196 (2005), p. 346-372. | MR | Zbl

[30] G. Tian & Z. Zhang - "On the Kähler-Ricci flow on projective manifolds of general type", Chinese Ann. Math. Ser. B 27 (2006), p. 179-192. | DOI | MR | Zbl

[31] G. Tian & X. Zhu - "Convergence of Kähler-Ricci flow", J. Amer. Math. Soc. 20 (2007), p. 675-699. | DOI | MR | Zbl

[32] H. Tsuji - "Existence and degeneration of Kähler-Einstein metrics on minimal algebraic varieties of general type", Math. Ann. 281 (1988), p. 123-133. | DOI | EuDML | MR | Zbl

[33] X.-J. Wang & X. Zhu - "Kähler-Ricci solitons on toric manifolds with positive first Chern class", Adv. Math. 188 (2004), p. 87-103. | MR | Zbl

[34] 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

[35] Z. Zhang - "On degenerate Monge-Ampère equations over closed Kähler manifolds", Int. Math. Res. Not. (2006), Art. ID 63640, 18. | MR | Zbl

[36] Z. Zhang, "Scalar curvature bound for Kähler-Ricci flows over minimal manifolds of general type", preprint arXiv:0801.3248. | DOI | MR | Zbl