On the envelope of holomorphy of a -sphere in

Authors:
Eric Bedford and Wilhelm Klingenberg

Journal:
J. Amer. Math. Soc. **4** (1991), 623-646

MSC:
Primary 32D10; Secondary 32E20

MathSciNet review:
1094437

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References | Similar Articles | Additional Information

**[Be]**Eric Bedford,*Levi flat hypersurfaces in 𝐶² with prescribed boundary: stability*, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)**9**(1982), no. 4, 529–570. MR**693779****[BG]**Eric Bedford and Bernard Gaveau,*Envelopes of holomorphy of certain 2-spheres in 𝐶²*, Amer. J. Math.**105**(1983), no. 4, 975–1009. MR**708370**, 10.2307/2374301**[Bi1]**Errett Bishop,*Differentiable manifolds in complex Euclidean space*, Duke Math. J.**32**(1965), 1–21. MR**0200476****[Bi2]**Errett Bishop,*Conditions for the analyticity of certain sets*, Michigan Math. J.**11**(1964), 289–304. MR**0168801****[Br]**Andrew Browder,*Cohomology of maximal ideal spaces*, Bull. Amer. Math. Soc.**67**(1961), 515–516. MR**0130580**, 10.1090/S0002-9904-1961-10663-0**[C]**E. M. Chirka,*Regularity of the boundaries of analytic sets*, Mat. Sb. (N.S.)**117(159)**(1982), no. 3, 291–336, 431 (Russian). MR**648411****[DG]**Amédée Debiard and Bernard Gaveau,*Problème de Dirichlet pour l’équation de Lévi*, Bull. Sci. Math. (2)**102**(1978), no. 4, 369–386 (French, with English summary). MR**517769****[E1]**Y. Eliashberg,*Three lectures on symplectic topology in Cala Gonone*, preprint.**[E2]**-,*Filling by holomorphic discs and its applications*, Geometry of Low-Dimensional Manifolds, London Math. Soc. Lecture Notes, vol. 151.**[EH]**Y. Eliashberg and V. Harlamov,*On the number of complex points on a real surface inside a complex surface*, Proceedings of the International Topology Conference in Leningrad, 1982, 143-148.**[F1]**Franc Forstnerič,*Analytic disks with boundaries in a maximal real submanifold of 𝐶²*, Ann. Inst. Fourier (Grenoble)**37**(1987), no. 1, 1–44 (English, with French summary). MR**894560****[F2]**Franc Forstnerič,*Polynomial hulls of sets fibered over the circle*, Indiana Univ. Math. J.**37**(1988), no. 4, 869–889. MR**982834**, 10.1512/iumj.1988.37.37042**[Fr1]**Michael Freeman,*The polynomial hull of a thin two-manifold*, Pacific J. Math.**38**(1971), 377–389. MR**0308442****[Fr2]**Michael Freeman,*The uniform algebra generated by 𝑧 and a smooth even function*, Math. Ann.**196**(1972), 269–274. MR**0310642****[GG]**M. Golubitsky and V. Guillemin,*Stable mappings and their singularities*, Springer-Verlag, New York-Heidelberg, 1973. Graduate Texts in Mathematics, Vol. 14. MR**0341518****[GW]**Stephen J. Greenfield and Nolan R. Wallach,*Extendibility properties of submanifolds of C2*, Proc. Carolina Conf. on Holomorphic Mappings and Minimal Surfaces (Chapel Hill, N.C., 1970) Dept. of Math., Univ. of North Carolina, Chapel Hill, N.C., 1970, pp. 77–85. MR**0287026****[G]**M. Gromov,*Pseudo holomorphic curves in symplectic manifolds*, Invent. Math.**82**(1985), 307-347.**[KW]**Carlos E. Kenig and Sidney M. Webster,*The local hull of holomorphy of a surface in the space of two complex variables*, Invent. Math.**67**(1982), no. 1, 1–21. MR**664323**, 10.1007/BF01393370**[K]**Wilhelm Klingenberg Jr.,*Asymptotic curves on real analytic surfaces in 𝐶²*, Math. Ann.**273**(1985), no. 1, 149–162. MR**814201**, 10.1007/BF01455920**[L]**H. Lewy,*The nature of the domain governed by different regimes*, Atti del Convegno Internazionale Metodi valutativi nella fisicamatematica, Accad. Naz. Lincei, 1975, 181-188.**[La]**Hon Fei Lai,*Real submanifolds of codimension two in complex manifolds*, Trans. Amer. Math. Soc.**264**(1981), no. 2, 331–352. MR**603767**, 10.1090/S0002-9947-1981-0603767-5**[Mi]**John Milnor,*Singular points of complex hypersurfaces*, Annals of Mathematics Studies, No. 61, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1968. MR**0239612****[Mo]**Jürgen Moser,*Analytic surfaces in 𝐶² and their local hull of holomorphy*, Ann. Acad. Sci. Fenn. Ser. A I Math.**10**(1985), 397–410. MR**802502**, 10.5186/aasfm.1985.1044**[MW]**Jürgen K. Moser and Sidney M. Webster,*Normal forms for real surfaces in 𝐶² near complex tangents and hyperbolic surface transformations*, Acta Math.**150**(1983), no. 3-4, 255–296. MR**709143**, 10.1007/BF02392973**[S]**E. L. Stout, Abstract 826-32-09**7**(1986), 174.

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DOI:
https://doi.org/10.1090/S0894-0347-1991-1094437-0

Article copyright:
© Copyright 1991
American Mathematical Society