@incollection{AST_2008__322__71_0, 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}, editor = {Hijazi Oussama}, series = {Ast\'erisque}, pages = {71--92}, publisher = {Soci\'et\'e math\'ematique de France}, number = {322}, year = {2008}, mrnumber = {2521654}, zbl = {1180.53067}, language = {en}, url = {http://www.numdam.org/item/AST_2008__322__71_0/} }
TY - CHAP AU - Tian, Gang TI - New results and problems on Kähler-Ricci flow BT - Géométrie différentielle, physique mathématique, mathématiques et société (II) - Volume en l'honneur de Jean-Pierre Bourguignon AU - Collectif ED - Hijazi Oussama T3 - Astérisque PY - 2008 SP - 71 EP - 92 IS - 322 PB - Société mathématique de France UR - http://www.numdam.org/item/AST_2008__322__71_0/ LA - en ID - AST_2008__322__71_0 ER -
%0 Book Section %A Tian, Gang %T New results and problems on Kähler-Ricci flow %B Géométrie différentielle, physique mathématique, mathématiques et société (II) - Volume en l'honneur de Jean-Pierre Bourguignon %A Collectif %E Hijazi Oussama %S Astérisque %D 2008 %P 71-92 %N 322 %I Société mathématique de France %U http://www.numdam.org/item/AST_2008__322__71_0/ %G en %F AST_2008__322__71_0
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://www.numdam.org/item/AST_2008__322__71_0/
[1] Deformation of Kähler metrics to Kähler-Einstein metrics on compact Kähler manifolds", Invent. Math. 81 (1985), p. 359-372. | DOI | EuDML | MR | Zbl
- "[2] Kähler-Ricci flow and the minimal model program for projective varieties", preprint arXiv:math.DG/0603064.
& - "[3] A note on uniformization of Riemann surfaces by Ricci flow", Proc. Amer. Math. Soc. 134 (2006), p. 3391-3393. | DOI | MR | Zbl
, & - "[4] Ricci flow on Kähler-Einstein surfaces", Invent. Math. 147 (2002), p. 487-544. | DOI | MR | Zbl
& - "[5] Ricci flow on Kähler-Einstein manifolds", Duke Math. J. 131 (2006), p. 17-73. | DOI | MR | Zbl
& , "[6] On the weak Kähler-Ricci flow", preprint arXiv:0802.0809. | MR | Zbl
, & - "[7] The Ricci flow on the -sphere", J. Differential Geom. 33 (1991), p. 325-334. | DOI | MR | Zbl
- "[8] Degenerate complex Monge-Ampère equations over compact Kähler manifolds", preprint arXiv:0710.5109. | DOI | MR | Zbl
& - "[9] Stability of bounded solutions for degenerate complex Monge-Ampère equations", preprint arXiv:0711.3643.
& - "[10] Classical solutions of fully nonlinear, convex, second-order elliptic equations", Comm. Pure Appl. Math. 35 (1982), p. 333-363. | DOI | MR | Zbl
- "[11] A priori -estimates for degenerate complex Monge-Ampère equations", preprint arXiv:0712.3743. | MR | Zbl
, & - "[12] Elliptic partial differential equations of second order, second ed., Grund. Math. Wiss., vol. 224, Springer, 1983. | MR | Zbl
& -[13] 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] 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] The cone of curves of algebraic varieties", Ann. of Math. 119 (1984), p. 603-633. | DOI | MR | Zbl
- "[16] Pluricanonical systems on minimal algebraic varieties", Invent. Math. 79 (1985), p. 567-588. | DOI | EuDML | MR | Zbl
, "[17] The complex Monge-Ampère equation", Acta Math. 180 (1998), p. 69-117. | DOI | MR | Zbl
- "[18] The entropy formula for the Ricci flow and its geometric applications", preprint arXiv:math.DG/0211159. | Zbl
- "[19] Perelman's argument for uniform bounded scalar curvature and diameter along the Kähler-Ricci flow", 2005, preprint.
& - "[20] The Kähler-Ricci flow on surfaces of positive Kodaira dimension", Invent. Math. 170 (2007), p. 609-653. | DOI | MR | Zbl
& - "[21]
& , in preparation.[22] Canonical measures and Kähler-Ricci flow", preprint arXiv:0802.2570. | DOI | MR | Zbl
& , "[23] On Kähler-Einstein metrics on certain Kähler manifolds with ", Invent. Math. 89 (1987), p. 225-246. | DOI | EuDML | MR | Zbl
- "[24] 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] 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] On Calabi's conjecture for complex surfaces with positive first Chern class", Invent. Math. 101 (1990), p. 101-172. | DOI | EuDML | MR | Zbl
, "[27] Kähler-Einstein metrics with positive scalar curvature", Invent. Math. 130 (1997), p. 1-37. | DOI | MR | Zbl
, "[28] 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] Moduli spaces of critical Riemannian metrics in dimension four", Adv. Math. 196 (2005), p. 346-372. | MR | Zbl
& - "[30] 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] Convergence of Kähler-Ricci flow", J. Amer. Math. Soc. 20 (2007), p. 675-699. | DOI | MR | Zbl
& - "[32] 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] Kähler-Ricci solitons on toric manifolds with positive first Chern class", Adv. Math. 188 (2004), p. 87-103. | MR | Zbl
& - "[34] 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] On degenerate Monge-Ampère equations over closed Kähler manifolds", Int. Math. Res. Not. (2006), Art. ID 63640, 18. | MR | Zbl
- "[36] Scalar curvature bound for Kähler-Ricci flows over minimal manifolds of general type", preprint arXiv:0801.3248. | DOI | MR | Zbl
, "