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.
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References
Bishop, E., “Differentiable manifolds in complex Euclidean space”, Duke Math. J. n (1965), 1–22.
Bochner, S., “Analutic and meromorphic continuation by means of Green's formula”, Ann. Math. 39 (1938), 14-19.
Greenfield, S., Cauchy-Riemann Equations in Several Variables (Bradeis Univ. thesis, 1967).
Hartogs, F., “Einige Folgerungen aus Cauchyschen Intergralformel bei Funktionen mehrer Veränderlichen” Silzb Mücnchener Akad., 36 (1906), 223.
Kohn, J. J., “Boundaries of complex manifolds”, Proceedings of the Conference on Complex Analysis (Springer-Verlag New York., 1965)
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.
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.
Lewy, H., “On hulls of holomorphy”, Comm. Pure Appl. Math., 13(1960), 587-591.
Martinelli, E., “Alcuni teoremi intergrali per le funzioni analitiche di piừ variabili complesse”, Rend. Accad Italia., 9(1939), 269–300.
Newlander, A., and Nirenberg, L., “Complex analytic coordinates in almost complex manifolds”, Ann. Math., 65(1957), 391–404.
Niremberg, L., “A complex Frobenius theorem”, Seminars on Analytic Functions (Institute for Advanced Study-United States Air Force Office of Scientific Research, 1957).
Rossi, H., report to appear in the Proceedings of the international Congress of Mathematicians (Moscow, 1966)
Weinstock, B., On Holomorphic Extension from Real Submanifolds of Complex Euclidean Space (M. I. T. thesis, 1966).
Wells, R.O., “On the local holomorphic hull of a real submanifold in several complex variables”, Comm. Pure Appl. Math., 19(1966), 145–165.
Wells, R.O, “Holomorphic approximation on real-analytic submanifolds of a complex manifold”, Proc. A. M. S., 17(1966), 1272–1275.
Wells, R.O, “Holomorphic hulls and holomorphic convexity of differentiable submanifolds”, to appear Trans. A. M.S
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Greenfield, S.J. (2011). Extendibility Properties of Real Submanifolds of Cn . In: Vesentini, E. (eds) Geometry of Homogeneous Bounded Domains. C.I.M.E. Summer Schools, vol 45. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11060-3_2
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DOI: https://doi.org/10.1007/978-3-642-11060-3_2
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