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Patrizio, Giorgio:
Foliazioni di Monge-Ampère e classificazione olomorfa
Bollettino dell'Unione Matematica Italiana Serie 8 8-B (2005), fasc. n.2, p. 299-321, Unione Matematica Italiana (Italian)
pdf (297 Kb), djvu (310 Kb). | MR2149386 | Zbl 1182.32011

Sunto

Si illustrano alcuni sviluppi della teoria delle foliazioni di Monge-Ampère e delle sue applicazioni alla classificazione delle varietà complesse non compatte.
Referenze Bibliografiche
[1] M. ABATE - G. PATRIZIO , Finsler Metrics - A Global Approach. (with applications to geometric function theory), Springer Lecture Notes n. 1591 Springer Verlag, Berlin (1994). | MR 1323428 | Zbl 0837.53001
[2] M. ABATE - G. PATRIZIO , Finsler Metrics - Kèlher Finsler manifolds of constant holomorphic curvature, Int. J. of Math., 8 (1997), 169-186. | MR 1442434 | Zbl 0891.53056
[3] R. AGUILAR - D. BURNS , On the algebraicization of certain Stein anifolds, Preprint 2001, arXiv:math.CV/0010287.
[4] L. V. AHLFORS , Conformal Invariants, Mc Graw Hill, New York (1973). | MR 357743 | Zbl 0272.30012
[5] A. F. BEARDON , A Primer on Riemann Surfaces, Cambridge University Press, Cambridge (1984). | MR 808581 | Zbl 0546.30001
[6] E. BEDFORD - D. BURNS , Holomorphic Mapping of Annuli in $\mathbb{C}^n$ and the Associated Extremal Function, Ann. Sc. Nor. Sup. Pisa, VI (1979), 381-414. | fulltext mini-dml | MR 553791 | Zbl 0422.32021
[7] E. BEDFORD - M. KALKA , Foliations and Complex Monge-Ampère Equations, Comm. Pure App. Math., 30 (1977), 543-571. | MR 481107 | Zbl 0351.35063
[8] E. BEDFORD - B. A. TAYLOR , A new capacity for plurisuharmonic functions, Acta Math., 149 (1982), 1-41. | MR 674165 | Zbl 0547.32012
[9] F. BERTELOOT - G. PATRIZIO , A Cartan theorem for proper holomorphic mappings of complete circular domains, Advances in Math., 153 (2000), 342-352. | MR 1770933 | Zbl 0962.32020
[10] J. BLAND - T. DUCHAMP , Moduli for Pointed Convex Domains, Invent. Math., 104 (1991), 61-112. | MR 1094047 | Zbl 0731.32010
[11] D. BURNS , Curvature of the Monge-Ampère foliation and parabolic manifolds, Ann. of Math., 115 (1982), 349-373. | MR 647810 | Zbl 0507.32011
[12] D. BURNS , On the Uniqueness and Characterization of Grauert Tubes, In Complex Analysis and Geometry, Dekker Lecture Notes in Pure and Appl. Math., 173 (1995), 119-133. | MR 1365971 | Zbl 0921.32006
[13] D. BURNS and R. HIND , Symplectic geometry and the uniqueness of Grauert tubes, Geom. and Funct. Anal., 11 (2001), 1-10. | MR 1829639 | Zbl 0980.32013
[14] D. BURNS - S. HALVERSCHEID - R. HIND , The geometry of Grauert tubes and complexification of symmetric spaces, Duke Math. J., 118 (2003), 465-491. | fulltext mini-dml | MR 1983038 | Zbl 1044.53039
[15] H. CARTAN , Les fonctions de deux variables complexes et le problème de représentation analytique, J. Math. Pures Appl., (9) 10 (1931), 1-114. | fulltext mini-dml
[16] J. P. DEMAILLY , Mesures de Moge-Ampère et caractérizasatio géométrique des variétés algébriques affines, Bull. Soc. Math. France, Memoire, 19 (1985). | fulltext mini-dml | MR 813252 | Zbl 0579.32012
[17] T. DUCHAMP - M. KALKA , Singular Monge-Ampére foliations, Math. Ann., 325 (2003), 187-209. | MR 1957270 | Zbl 1050.53062
[18] J. E. FORNAESS - N. SIBONY , Complex dynamics in higher dimensions, Complex Potential Theory, NATO ASI Series, Mathematical and Physical Sciences-Vol. 439 (1994), 131-186. | MR 1332961 | Zbl 0811.32019
[19] V. GUILLEMIN - M. STENZEL , Grauert Tubes and the Homogeneous Monge-Ampère Equation, J. of Diff. Geometry, 34 (1991), 561-570. | fulltext mini-dml | MR 1131444 | Zbl 0746.32005
[20] H. GRAUERT , On Levi's problem and the imbedding of real-analytic manifolds, Ann. Math., 68 (1958), 460-472. | MR 98847 | Zbl 0108.07804
[21] R. E. GREENE - G. KRANTZ , Deformation of Complex Structures, estimates of $\bar\partial$ Equation and Stabilty of the Bergmann Kernel, Adv. of Math., 43 (1982), 1-86. | MR 644667 | Zbl 0504.32016
[22] S. HALVERSCHEID , Maximal domains of definiton of adapted complex structures of symmetric spaces of non-compact type, Schriftenreihe des Graduiertenkollegs Geometrie und Mathematische Physik, 39 (2001) Bochum: Univ. Bochum, Institut für Mathematik. | Zbl 0985.32010
[23] S. HALVERSCHEID - A. IANNUZZI , Maximal complexifications of certain homogeneous Riemannian manifolds, Trans. Am. Math. Soc., 355 (2003), 4581-4594. | MR 1990763 | Zbl 1039.32009
[24] A. T. HUCKLEBERRY - J. A. WOLF , Cycles Spaces of Flag Domains: A Complex Geometric Viewpoint, Preprint 2002, arXiv:math.RT/0210445. | fulltext mini-dml | MR 1922101 | Zbl 1084.22011
[25] M. KALKA - G. PATRIZIO , Polynomial Solutions of the Complex Homogeneous Monge-Ampère Equation, Michigan Math. J., 52 (2004), 243-251. | fulltext mini-dml | MR 2069798 | Zbl 1058.32024
[26] SU-JEN KAN , On rigidity of Grauert tubes over homogeneous Riemannian manifolds, To appear in J. reine angew. Math. | fulltext mini-dml | MR 2108219 | Zbl 1069.53040
[27] M. KLIMEK , Pluripotential Theory, London Mathematical Society Monographs New Series, 6, Oxford (1991). | MR 1150978 | Zbl 0742.31001
[28] P. KOEBE , Über die Uniformisierung beliebiger analityscher Kurven, Göttinger Nachr. (1907), 191-210 e 633-669.
[29] L. LEMPERT , La métrique de Kobayashi et la représantation des domaines sur la boule, Bull. Soc. Math. France, 109 (1989), 427-474. | fulltext mini-dml | MR 660145 | Zbl 0492.32025
[30] L. LEMPERT , Complex Structures on the Tangent Bundle of Riemannian Manifolds, In Complex Analysis an and geometry, Plenum Press, (1993), 235-251. | MR 1211884 | Zbl 0798.53040
[31] L. LEMPERT , Holomorphic invariants, normal forms, and the moduli space of convex domains, Annals of Math., 128 (1988), 43-78. | MR 951507 | Zbl 0658.32015
[32] L. LEMPERT , R. SZÖKE , Global Solutions of the Homogeneous Complex Monge-Ampère Equation and Complex Structures on the Tangent Bundle of Riemannian Manifolds, Math. Ann., 290 (1991), 689-712. | MR 1119947 | Zbl 0752.32008
[33] Y. MATSUSHIMA , On tube domains, In Symmetric Spaces, short Courses presented at Washington Univ., Pure appl. Math. 8, Dekker, New York (1972), 255-270. | MR 402135 | Zbl 0232.32001
[34] G. PATRIZIO Parabolic Exhaustions for Strictly Convex Domains, Manuscripta Math., 47 (1984), 271-309. | MR 744324 | Zbl 0581.32018
[35] G. PATRIZIO , A Characterization of Complex Manifolds Biholomorphic to a Circular Domain, Math. Z., 189 (1985), 343-363. | MR 783561 | Zbl 0591.32030
[36] G. PATRIZIO - P. M. WONG , Stability of the Monge-Amère Foliation, Math. Ann., 263 (1983), 13-29. | MR 697327 | Zbl 0512.32013
[37] G. PATRIZIO - P. M. WONG , On Stein Manifolds with Compact Symmetric Center, Math. Ann., 289 (1991), 355-382. | MR 1096176 | Zbl 0729.32003
[38] G. PATRIZIO - A. TOMASSINI , A Characterization of Affine Hyperquadrics, To appear in Annali di Matematica Pura e App. | Zbl pre05058524
[39] H. POINCARÉ , Les fonctions analytiques de deux variables et la représantation conforme, Rend.Circ. Matem. Palermo, 23 (1907), 185-220.
[40] H. POINCARÉ , Sur l'uniformisation des fonctions analytiques, Acta Math., 31 (1908), 1-63. | MR 1555036
[41] W. STOLL , The Characterization of Strictly Parabolic Manifolds, Ann. Sc. Nor. Sup. Pisa, VII (1980), 87-154. | fulltext mini-dml | MR 577327 | Zbl 0438.32005
[42] R. SZÖKE , Complex Structures on the Tangent Bundle of Riemannian Manifolds, Math. Ann., 291 (1991), 409-428. | MR 1133340 | Zbl 0749.53021
[43] R. SZÖKE , Adapted Complex Structures and Riemannian homogeneous spaces, Ann. Pol. Math., LXX (1998), 215-220. | MR 1668726 | Zbl 0966.53038
[44] B. TOTARO , Complexifications of nonnegatively curved manifolds, J. Eur. Math. Soc. (JEMS), 5 (2003), 69-94. | MR 1961135 | Zbl 1040.32006
[45] E. VESENTINI , Variations on a theme of Carathéodory, Ann. Sc. Nor. Sup. Pisa, VI (1979), 39-68. | fulltext mini-dml | MR 529475 | Zbl 0413.46039
[46] E. VESENTINI , Complex geodesics, Comp. Math., 44 (1981), 375-394. | fulltext mini-dml | MR 662466 | Zbl 0488.30015
[47] H. WHITNEY - F. BRUHAT , Quelques propriétés fondamentales des ensembles analytiques-réels, Comment. Math. Helv., 22 (1959), 132-160. | MR 102094 | Zbl 0100.08101
[48] P. M. WONG , Geometry of the homogeneous complex Monge-Ampère equation, Inv. Math., 67 (1982), 261-274. | MR 665157 | Zbl 0555.32009
[49] P. M. WONG , On Umbilical Hypersurfaces and Uniformization of Circular Domains, Proc. Symp. in Pure Math., 41 (1984), 225-252. | MR 740886 | Zbl 0587.32029

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