## On the H. Lewy extension phenomenon.(English)Zbl 0241.32006

### MSC:

 32E99 Holomorphic convexity 35N15 $$\overline\partial$$-Neumann problems and formal complexes in context of PDEs 32F99 Geometric convexity in several complex variables
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### References:

 [1] Aldo Andreotti and Hans Grauert, Théorème de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France 90 (1962), 193 – 259 (French). · Zbl 0106.05501 [2] Aldo Andreotti and Edoardo Vesentini, Carleman estimates for the Laplace-Beltrami equation on complex manifolds, Inst. Hautes Études Sci. Publ. Math. 25 (1965), 81 – 130. · Zbl 0138.06604 [3] Errett Bishop, Differentiable manifolds in complex Euclidean space, Duke Math. J. 32 (1965), 1 – 21. · Zbl 0154.08501 [4] S. J. Greenfield, Cauchy-Riemann equations in several variables, Ann. Scuola Norm. Sup. Pisa (3) 22 (1968), 275 – 314. · Zbl 0159.37502 [5] Stephen J. Greenfield, Upper bounds on the dimension of extendibility of submanifolds in \?$$^{n}$$, Proc. Amer. Math. Soc. 23 (1969), 185 – 189. · Zbl 0188.39104 [6] Lars Hörmander, \?² estimates and existence theorems for the \partial operator, Acta Math. 113 (1965), 89 – 152. · Zbl 0158.11002 [7] Lars Hörmander, An introduction to complex analysis in several variables, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. · Zbl 0271.32001 [8] J. J. Kohn and Hugo Rossi, On the extension of holomorphic functions from the boundary of a complex manifold, Ann. of Math. (2) 81 (1965), 451 – 472. · Zbl 0166.33802 [9] 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. · Zbl 0074.06204 [10] Hans Lewy, On hulls of holomorphy, Comm. Pure Appl. Math. 13 (1960), 587 – 591. · Zbl 0113.06102 [11] B. Malgrange, Ideals of differentiable functions, Tata Institute of Fundamental Research Studies in Mathematics, No. 3, Tata Institute of Fundamental Research, Bombay; Oxford University Press, London, 1967. · Zbl 0177.17902 [12] Ricardo Nirenberg, Function algebras on a class of pseudoconvex submanifolds of \?$$^{n}$$, Boll. Un. Mat. Ital. (4) 3 (1970), 628 – 636 (English, with Italian summary). · Zbl 0202.36701 [13] Ricardo Nirenberg and R. O. Wells Jr., Approximation theorems on differentiable submanifolds of a complex manifold, Trans. Amer. Math. Soc. 142 (1969), 15 – 35. · Zbl 0188.39103 [14] Hugo Rossi, Holomorphically convex sets in several complex variables, Ann. of Math. (2) 74 (1961), 470 – 493. · Zbl 0107.28601 [15] Труды международного конгресса математиков (Москва, 1966), Едитед бы И. Г. Петровский, Издат. ”Мир”, Мосцощ, 1968 (Руссиан). [16] Giuseppe Tomassini, Tracce delle funzioni olomorfe sulle sottovarietà analitiche reali d’una varietà complessa, Ann. Scuola Norm. Sup. Pisa (3) 20 (1966), 31 – 43 (Italian). · Zbl 0154.33501 [17] B. Weinstock, On holomorphic extension from real submanifolds of complex Euclidean space, Thesis, Massachusetts Institute of Technology, Cambridge, Mass., 1966. [18] 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. · Zbl 0142.33901 [19] R. O. Wells Jr., Holomorphic hulls and holomorphic convexity, Rice Univ. Studies 54 (1968), no. 4, 75 – 84. · Zbl 0177.11402
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