Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A totally real three-sphere in $ {\bf C}\sp 3$ bounding a family of analytic disks


Author: Franc Forstnerič
Journal: Proc. Amer. Math. Soc. 108 (1990), 887-892
MSC: Primary 32F25; Secondary 32E20
DOI: https://doi.org/10.1090/S0002-9939-1990-1038758-7
MathSciNet review: 1038758
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We construct a smoothly embedded totally real three-sphere $ S$ in $ {{\mathbf{C}}^3}$ and a one-parameter family of analytic disks in $ {{\mathbf{C}}^3}$ that have boundaries in $ S$.


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

  • [1] H. Alexander, A note on polynomially convex hulls, Proc. Amer. Math. Soc. 33 (1972), 389-391. MR 0294689 (45:3757)
  • [2] P. Ahern and W. Rudin, Totally real embeddings of $ {S^3}$ into $ {{\mathbf{C}}^3}$, Proc. Amer. Math. Soc. 94 (1985), 460-462. MR 787894 (86g:32031)
  • [3] E. Bishop, Differentiable manifolds in complex Euclidean spaces, Duke Math. J. 32 (1965), 1-21. MR 0200476 (34:369)
  • [4] E. M. Čirka, Regularity of the boundaries of analytic sets, Mat. Sb. (NS) 117 (1982), 291-334; English transl., Math. USSR Sb. 45 (1983), 291-336. MR 648411 (83f:32009)
  • [5] F. Forstnerič, On totally real embeddings into $ {C^n}$, Exposition Math. 4 (1986), 243-255. MR 880125 (88g:32016)
  • [6] -, Some totally real embeddings of three-manifolds, Manuscripta Math. 55 (1986), 1-7. MR 828408 (88f:32059)
  • [7] M. Gromov, Convex integration of differential relations. I, Izv. Akad. Nauk SSSR 37 (1973); English transl., Math. USSR Izv. 7 (1973), 329-343. MR 0413206 (54:1323)
  • [8] -, Partial differential relations, Springer-Verlag, Berlin and New York, 1986. MR 864505 (90a:58201)
  • [9] D. C. Hill and G. Taiani, Families of analytic disks in $ {{\mathbf{C}}^n}$ with boundaries in a prescribed CR manifold, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 5 (1978), 327-380. MR 501906 (80c:32023)
  • [10] J. A. Lees, On the classification of lagrange immersions, Duke Math. J. 43 (1976), 217-224. MR 0410764 (53:14509)
  • [11] M. Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347. MR 809718 (87j:53053)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 32F25, 32E20

Retrieve articles in all journals with MSC: 32F25, 32E20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1038758-7
Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society