Holomorphic hulls and holomorphic convexity of differentiable submanifolds

Wells, R. O.

doi:10.1090/S0002-9947-1968-0222340-8

Holomorphic hulls and holomorphic convexity of differentiable submanifolds
HTML articles powered by AMS MathViewer

by R. O. Wells

Trans. Amer. Math. Soc. 132 (1968), 245-262

DOI: https://doi.org/10.1090/S0002-9947-1968-0222340-8

PDF | Request permission

References

Errett Bishop, Differentiable manifolds in complex Euclidean space, Duke Math. J. 32 (1965), 1–21. MR 200476
Errett Bishop, A minimal boundary for function algebras, Pacific J. Math. 9 (1959), 629–642. MR 109305
R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
Michael Freeman, Some conditions for uniform approximation on a manifold, Function Algebras (Proc. Internat. Sympos. on Function Algebras, Tulane Univ., 1965) Scott-Foresman, Chicago, Ill., 1966, pp. 42–60. MR 0193538
Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. MR 0180696
Lars Hörmander, An introduction to complex analysis in several variables, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR 0203075
Hellmuth Kneser, Die Randwerte einer analytischen Funktion zweier Veränderlichen, Monatsh. Math. Phys. 43 (1936), no. 1, 364–380 (German). MR 1550538, DOI 10.1007/BF01707615
Robert Hermann, Convexity and pseudoconvexity for complex manifolds, J. Math. Mech. 13 (1964), 667–672. MR 0167995
Hans Lewy, On the local character of the solutions of an atypical linear differential equation in three variables and a related theorem for regular functions of two complex variables, Ann. of Math. (2) 64 (1956), 514–522. MR 81952, DOI 10.2307/1969599
Hans Lewy, On hulls of holomorphy, Comm. Pure Appl. Math. 13 (1960), 587–591. MR 150339, DOI 10.1002/cpa.3160130403
Ricardo Nirenberg and R. O. Wells Jr., Holomorphic approximation on real submanifolds of a complex manifold, Bull. Amer. Math. Soc. 73 (1967), 378–381. MR 209850, DOI 10.1090/S0002-9904-1967-11760-9
Hugo Rossi, Holomorphically convex sets in several complex variables, Ann. of Math. (2) 74 (1961), 470–493. MR 133479, DOI 10.2307/1970292
Hugo Rossi, On envelopes of holomorphy, Comm. Pure Appl. Math. 16 (1963), 9–17. MR 148940, DOI 10.1002/cpa.3160160103
Jean-Pierre Serre, Quelques problèmes globaux relatifs aux variétés de Stein, Colloque sur les fonctions de plusieurs variables, tenu à Bruxelles, 1953, Georges Thone, Liège; Masson & Cie, Paris, 1953, pp. 57–68 (French). MR 0064155
Friedrich Sommer, Komplex-analytische Blätterung reeller Mannigfaltigkeiten im $C^{n}$, Math. Ann. 136 (1958), 111–133 (German). MR 101924, DOI 10.1007/BF01362293
Karl Stein, Zur Theorie der Funktionen mehrerer komplexer Veränderlichen, Math. Ann. 114 (1937), no. 1, 543–569 (German). MR 1513157, DOI 10.1007/BF01594195
R. O. Wells Jr., On the local holomorphic hull of a real submanifold in several complex variables, Comm. Pure Appl. Math. 19 (1966), 145–165. MR 197785, DOI 10.1002/cpa.3160190204
R. O. Wells Jr., Locally holomorphic sets, J. Analyse Math. 17 (1966), 337–345. MR 214806, DOI 10.1007/BF02788663
R. O. Wells Jr., Holomorphic approximation on real-analytic submanifolds of a complex manifold, Proc. Amer. Math. Soc. 17 (1966), 1272–1275. MR 200946, DOI 10.1090/S0002-9939-1966-0200946-3