Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)

 
 

 

On the envelope of holomorphy of a $ 2$-sphere in $ {\bf C}\sp 2$


Authors: Eric Bedford and Wilhelm Klingenberg
Journal: J. Amer. Math. Soc. 4 (1991), 623-646
MSC: Primary 32D10; Secondary 32E20
DOI: https://doi.org/10.1090/S0894-0347-1991-1094437-0
MathSciNet review: 1094437
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [Be] E. Bedford, Levi flat hypersurfaces in $ {\mathbb{C}^2}$ with prescribed boundary: stability, Ann. Scuola Norm. Sup. Pisa. IX (1982), 529-570. MR 693779 (85d:32029)
  • [BG] E. Bedford and B. Gaveau, Envelopes of holomorphy of certain $ 2$-spheres in $ {\mathbb{C}^2}$, Amer. J. Math. 105 (1983), 975-1009. MR 708370 (84k:32016)
  • [Bi1] E. Bishop, Differentiable manifolds in complex Euclidean space, Duke Math. J. 32 (1965), 1-22. MR 0200476 (34:369)
  • [Bi2] -, Conditions for the analyticity of certain sets, Michigan Math. J. 11 (1964), 289-304. MR 0168801 (29:6057)
  • [Br] A. Browder, Cohomology of maximal ideal spaces, Bull. Amer. Math. Soc. 67 (1961), 515-516. MR 0130580 (24:A440)
  • [C] E. Chirka, Regularity of the boundaries of analytic sets, Math. USSR Sbornik 45 (1983), 291-335. MR 648411 (83f:32009)
  • [DG] A. Debiard and B. Gaveau, Problème de Dirichlet pour l'équation de Lévi, Bull. Sci. Math. 102 (1978), 369-386. MR 517769 (80f:32010)
  • [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] F. Forstneric, Stability of analytic disks with boundaries in totally real submanifold of $ {\mathbb{C}^2}$, Ann. Inst. Fourier 37 (1987), 1-44. MR 894560 (88j:32019)
  • [F2] -, Polynomial hulls of sets fibered over the circle, Indiana Univ. Math. J. 37 (1988), 869-889. MR 982834 (90g:32018)
  • [Fr1] M. Freeman, The polynomial hull of a thin two-manifold, Pacific J. Math 38 (1971), 377-389. MR 0308442 (46:7556)
  • [Fr2] -, The uniform algebra generated by $ z$ and a smooth even function, Math. Ann. 196 (1972), 269-274. MR 0310642 (46:9740)
  • [GG] M. Golubitsky and V. Guillemin, Stable mappings and their singularities, Springer-Verlag New York, Heidelberg, and Berlin, 1973. MR 0341518 (49:6269)
  • [GW] S. Greenfield and N. Wallach, Extendibility properties of submanifolds of $ {\mathbb{C}^2}$, Proceedings of North Carolina Conference on Holomorphic Mappings and Minimal Surfaces, 1970. MR 0287026 (44:4233)
  • [G] M. Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347.
  • [KW] C. Kenig and S. Webster, The local hull of holomorphy of a surface in the space of two complex variables, Invent. Math. 67 (1982), 1-21. MR 664323 (84c:32014)
  • [K] W. Klingenberg, Asymptotic curves on real analytic surfaces in $ {\mathbb{C}^2}$, Math. Ann. 273 (1985), 149-162. MR 814201 (87f:32047)
  • [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] H. F. Lai, Real submanifolds of codimension two in complex manifolds, Trans. Amer. Math. Soc. 264 (1981), 331-352. MR 603767 (82c:53023)
  • [Mi] J. Milnor, Singular points of complex hypersurfaces, Princeton Univ. Press, Princeton, NJ, 1968. MR 0239612 (39:969)
  • [Mo] J. Moser, Analytic surfaces in $ {\mathbb{C}^2}$ and their local hull of holomorphy, Ann. Acad. Sci. Fenn. Ser. A. I. Math. 10 (1985), 397-410. MR 802502 (87c:32024)
  • [MW] J. Moser and S. Webster, Normal forms for real surfaces in $ {\mathbb{C}^2}$ near complex tangents and hyperbolic surface transformations, Acta Math. 150 (1983), 255-296. MR 709143 (85c:32034)
  • [S] E. L. Stout, Abstract 826-32-09 7 (1986), 174.

Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC: 32D10, 32E20

Retrieve articles in all journals with MSC: 32D10, 32E20


Additional Information

DOI: https://doi.org/10.1090/S0894-0347-1991-1094437-0
Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society