Open Access

The disk property. A short survey

   | May 17, 2013
Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică's Cover Image
Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică
Proceedings of the 10th International Workshop on Differential Geometry and its Applications

Cite

[1] M. Colţoiu: Coverings of 1-convex manifolds with 1-dimensional excep- tional set. Comment. Math. Helv. 68 (1993), no. 3, 469-479.Search in Google Scholar

[2] M. Colţoiu; C. Joiţa: The disk property of coverings of 1-convex surfaces. Proc. Amer. Math. Soc. 140 (2012), no. 2, 575-580.Search in Google Scholar

[3] M. Colţoiu; C. Joiţa: Convexity properties of coverings of 1-convex sur- faces. Preprint, arXiv:1110.5791vl.Search in Google Scholar

[4] M. Colţoiu; J. Ruppenthal: On Hartogs’ extension theorem on (n - 1)- complete complex spaces. J. Reine Angew. Math. 637 (2009), 41-47.10.1515/CRELLE.2009.089Search in Google Scholar

[5] M. Colţoiu; M. Tibăr: On the disk theorem. Math. Ann. 345 (2009), no. 1, 175-183.Search in Google Scholar

[6] F. Docquier; H. Grauert: Levisches Problem und Rungescher Satz fur Teilgebiete Steinscher Mannigfaltigkeiten. Math. Ann. 140 (1960), 94-12310.1007/BF01360084Search in Google Scholar

[7] P. Eyssidieux; L. Katzarkov; T. Pantev; M. Ramachandran: Linear Sha- farevich Conjecture. Preprint, arXiv:0904.0693.Search in Google Scholar

[8] G. Elencwajg: Pseudo-convexite locale dans les varietes kahleriennes. Ann. Inst. Fourier (Grenoble) 25 (1975), no. 2, 295-314.Search in Google Scholar

[9] L. Ehrenpreis: A new proof and an extension of Hartogs’ theorem. Bull. Amer. Math. Soc. 67 (1961), 507-509, .Search in Google Scholar

10] J. E. Fornaess: 2 dimensional counterexamples to generalizations of the Levi problem. Math. Ann. 230 (1977), no. 2, 169-173.Search in Google Scholar

11] J. E.Fornaess; R. Narasimhan: The Levi problem on complex spaces with singularities. Math. Ann. 248 (1980), no. 1, 47-72. Search in Google Scholar

12] F. Hartogs: Einige Folgerungcn aus der Cauchyschen Intcgmlformel bei Funktionen mehrerer Veranderlichen, Baycrischc Akademie der Wis- senschaften. Mathematish-Physikalisch Klasse, 36 (1906), 223-292.Search in Google Scholar

13] A. Hirschowitz: Pseudoconvexite au-dessus d’espaces plus ou moins ho- mogenes. Invent. Math. 26 (1974), 303-322.10.1007/BF01425555Search in Google Scholar

14] F. Lárusson; R. Sigurdsson: Plurisubharmonic functions and analytic discs on manifolds. J. Reine Angew. Math. 501 (1998), 1-39.10.1515/crll.1998.078Search in Google Scholar

15] F. Lárusson; R. Sigurdsson: Plurisubharmonicity of envelopes of disc functionals on manifolds. J. Reine Angew. Math. 555 (2003), 27-38.10.1515/crll.2003.013Search in Google Scholar

16] E.E. Levi: Studii sui punti singolari essenziali delle funzioni analitiche di due o piu variabili complesse. Annali di Matematica Pura e Applicata, 17 (1910), 61-87.10.1007/BF02419336Search in Google Scholar

17] J. Merker; E. Porten: A Morse-theoretical proof of the Hartogs extension theorem. J. Geom. Anal. 17 (2007), no. 3, 513-546.Search in Google Scholar

18] J. Merker; E. Porten: The Hartogs extension theorem on (n - Incomplete complex spaces. J. Reine Angew. Math. 637 (2009), 23-39.10.1515/CRELLE.2009.088Search in Google Scholar

19] W.F. Osgood: Lehrbuch der Funktionentheońe, Bd II, B.G. Teubner, Leipzig, (1929).Search in Google Scholar

20] N. 0vrelid; S. Vassiliadou: Semiglobal results for d on complex spaces with arbitrary singularities, Part II. Trans. Amer. Math. Soc. 363 (2011), no. 12, 6177-6196Search in Google Scholar

21] E. A. Poletsky: Pluńsubharmonic functions as solutions of vanational problems, Several complex variables and complex geometry (Santa Cruz, CA, 1989), Proc. Sympos. Pure Math., 52, Part 1, Amer. Math. Soc., 1991, pp. 163-171.10.1090/pspum/052.1/1128523Search in Google Scholar

[22] E. A. Poletsky: The minimum principle. Indiana Univ. Math. J. 51 (2002), 269-303.10.1512/iumj.2002.51.2214Search in Google Scholar

[23] J.-P. Rosay: Poletsky theory of disks on holomorphic manifolds. Indiana Univ. Math. J. 52 (2003), no. 1, 157-169.Search in Google Scholar

[24] O. Suzuki: Pseudoconvex domains on a Kähler manifold with posi- tive holomorphic bisectional curvature. Publ. Res. Inst. Math. Sci. 12 (1976/77), no. 1, 191-214.10.2977/prims/1195190963Search in Google Scholar

[25] A. Takeuchi: Domaines pseudoconvexes sur les variétés Kählériénnés. J. Math. Kyoto Univ. 6 (1967), 323-357. 10.1215/kjm/1250524335Search in Google Scholar

eISSN:
1844-0835
Language:
English
Publication timeframe:
Volume Open
Journal Subjects:
Mathematics, General Mathematics