Geometry of Homogeneous Bounded Domains pp 89-108 | Cite as
Extendibility Properties of Real Submanifolds of Cn
Chapter
Abstract
In 1906 F.Hartogs [4] discovered that a function analytic in a neighborhood of the bicyclinder in C2 could always be extended to an analytic function defined in a neighborhood of all the bicyclinder. Not much later (1910) E.E.Levi [6] found a local analogue of Hartogs’ result: let h: C2 →R be differentiable and suppose that M = h-1 (0) is a submanifold of C2.
Keywords
Vector Bundle Complex Manifold Real Hypersurface Fundamental System Analytic Disc
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- 1.Bishop, E., “Differentiable manifolds in complex Euclidean space”, Duke Math. J. n (1965), 1–22.Google Scholar
- 2.Bochner, S., “Analutic and meromorphic continuation by means of Green's formula”, Ann. Math. 39 (1938), 14-19.MathSciNetCrossRefGoogle Scholar
- 3.Greenfield, S., Cauchy-Riemann Equations in Several Variables (Bradeis Univ. thesis, 1967).Google Scholar
- 4.Hartogs, F., “Einige Folgerungen aus Cauchyschen Intergralformel bei Funktionen mehrer Veränderlichen” Silzb Mücnchener Akad., 36 (1906), 223. Google Scholar
- 5.Kohn, J. J., “Boundaries of complex manifolds”, Proceedings of the Conference on Complex Analysis (Springer-Verlag New York., 1965)Google Scholar
- 6.Levi, E. E., “Studii sui punti singolari essenziali delle funzioni di due o piừ variabili complesse”, Annali di Mat. Pura ed appl., 3(1910) 61–87.Google Scholar
- 7.Lewy, H., “On the local character of the solution of an atypical linear differential equation in three variables and a related theorem for regular functions of two complex variables”, Ann. Math., 64(1956), 514–522.MathSciNetCrossRefGoogle Scholar
- 8.Lewy, H., “On hulls of holomorphy”, Comm. Pure Appl. Math., 13(1960), 587-591. MathSciNetMATHCrossRefGoogle Scholar
- 9.Martinelli, E., “Alcuni teoremi intergrali per le funzioni analitiche di piừ variabili complesse”, Rend. Accad Italia., 9(1939), 269–300.Google Scholar
- 10.Newlander, A., and Nirenberg, L., “Complex analytic coordinates in almost complex manifolds”, Ann. Math., 65(1957), 391–404.MathSciNetCrossRefGoogle Scholar
- 11.Niremberg, L., “A complex Frobenius theorem”, Seminars on Analytic Functions (Institute for Advanced Study-United States Air Force Office of Scientific Research, 1957).Google Scholar
- 12.Rossi, H., report to appear in the Proceedings of the international Congress of Mathematicians (Moscow, 1966)Google Scholar
- 13.Weinstock, B., On Holomorphic Extension from Real Submanifolds of Complex Euclidean Space (M. I. T. thesis, 1966).Google Scholar
- 14.Wells, R.O., “On the local holomorphic hull of a real submanifold in several complex variables”, Comm. Pure Appl. Math., 19(1966), 145–165.MATHCrossRefGoogle Scholar
- 15.Wells, R.O, “Holomorphic approximation on real-analytic submanifolds of a complex manifold”, Proc. A. M. S., 17(1966), 1272–1275.MATHCrossRefGoogle Scholar
- 16.Wells, R.O, “Holomorphic hulls and holomorphic convexity of differentiable submanifolds”, to appear Trans. A. M.SGoogle Scholar
Copyright information
© Springer-Verlag Berlin Heidelberg 2011