Identyfikatory
Warianty tytułu
Konferencja
2nd Forum of Polish Mathematicians (2 ; 01.07.2008 ; Częstochowa, Polska)
Języki publikacji
Abstrakty
We discuss two cases when the complex Monge-Ampere equation appears in Kähler geometry: the Calabi conjecture (with its solution by Yau) and the equation for geodesics in the Mabuchi space of Kähler metrics, introduced independently by Semmes and Donaldson.
Rocznik
Tom
Strony
5--13
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
autor
- Jagiellonian University, Zbigniew.Blocki@im.uj.edu.pl
Bibliografia
- [1] Aubin T., Equations du type de Monge-Ampère sur les variétés Kähleriennes compactes, C.R. Acad. Sci. Paris 283 (1976), 119-121.
- [2] Błocki Z., Regularity of the degenerate Monge-Ampère equation on compact Kähler manifolds, Math. Z. 244 (2003), 153-161.
- [3] Błocki Z., Uniqueness and stability for the Monge-Ampère equation on compact Kähler manifolds, Indiana Univ. Math. J. 52 (2003), 1697-1702.
- [4] Błocki Z., On uniform estimate in Calabi-Yau theorem, Sci. China Ser. A 48 suppl. (2005), 244-247.
- [5] Błocki Z., The Monge-Ampère equation on compact Kähler manifolds, unpublihed lecture notes based on the course given at Winter School in Complex Analysis, Toulouse, 2005, available at http://gamma.im.uj.edu.pl/~blocki/
- [6] Błocki Z., A gradient estimate in the Calabi-Yau theorem, preprint, 2008.
- [7] Caffarelli L., Kohn J.J., Nirenberg L., Spruck J., The Dirichlet problem for nonlinear second order elliptic equations. II. Complex Monge-Ampère, and uniformly elliptic, equations, Comm. Pure Appl. Math. 38 (1985), 209-252.
- [8] Calabi E., The space of Kähler metrics, Proc. Internat. Congress Math. Amsterdam 1954, vol. 2, 206-207.
- [9] Chen X.X., The space of Kähler metrics, J. Diff. Geom. 56 (2000), 189-234.
- [10] Demailly J.P., Complex Analytic and Differential Geometry, 1997, available at http://wwwfourier.ujf-grenoble.fr/~demailly/books.html
- [11] Donaldson S.K., Symmetric spaces, Kähler geometry and Hamiltonian dynamics, Northern California Symplectic Geometry Seminar, 13-33, Amer. Math. Soc. Transl. Ser. 2, 196, Amer. Math. Soc., Providence, RI, 1999.
- [12] Donaldson S.K., Scalar curvature and stability of toric varieties, J. Diff. Geom. 62 (2002), 289-349.
- [13] Gamelin T.W., Sibony N., Subharmonicity for uniform algebras, J. Funct. Anal. 35 (1980), 64-108.
- [14] Hörmander L., An Introduction to Complex Analysis in Several Variables, 3rd ed., North-Holland, Amsterdam 1990.
- [15] Kołodziej S., The complex Monge-Ampère equation, Acta Math. 180 (1998), 69-117.
- [16] Mabuchi T., Some symplectic geometry on compact Kähler manifolds. I, Osaka J. Math. 24 (1987), 227-252.
- [17] Newlander A., Nirenberg L., Complex analytic coordinates in almost complex manifolds, Ann. of Math. 65 (1957), 391-404.
- [18] Pliś S., A counterexample to the regularity of the degenerate complex Monge-Ampère equation, Ann. Polon. Math. 86 (2005), 171-175.
- [19] Semmes S., Complex Monge-Ampère and symplectic manifolds, Amer. J. Math. 114 (1992), 495-550.
- [20] Yau S.-T., On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation, Comm. Pure Appl. Math. 31 (1978), 339-411.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPC6-0014-0001