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The hull of Rudin's Klein bottle


Author: John T. Anderson
Journal: Proc. Amer. Math. Soc. 140 (2012), 553-560
MSC (2010): Primary 32E20; Secondary 32V40
DOI: https://doi.org/10.1090/S0002-9939-2011-10998-5
Published electronically: June 2, 2011
MathSciNet review: 2846323
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Abstract: In 1981 Walter Rudin exhibited a totally real embedding of the Klein bottle into $ \mathbb{C}^2$. We show that the polynomially convex hull of Rudin's Klein bottle contains an open subset of $ \mathbb{C}^2$. We also describe another totally real Klein bottle in $ \mathbb{C}^2$ whose hull has topological dimension equal to three.


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

  • 1. H. Alexander and J. Wermer, Polynomial Hulls with Convex Fibers, Math. Ann. 271 (1985), 99-109. MR 779607 (86i:32025)
  • 2. J. Anderson, On an Example of Ahern and Rudin, Proc. A.M.S. 116, no. 3 (1992), 695-699. MR 1129870 (93c:32021)
  • 3. A. Derdzinski and T. Januszkiewicz, Totally Real Immersions of Surfaces, Trans. A.M.S. 362, no. 1 (2010), 53-115. MR 2550145 (2010j:53108)
  • 4. J. Duval and D. Gayet, Riemann Surfaces and Totally Real Tori, arXiv:math.cv/0910.2139
  • 5. F. Forstnerič, Complex Tangents of Real Surfaces in Complex Surfaces, Duke Math. J. 67, no. 2 (1992), 353-376. MR 1177310 (93g:32025)
  • 6. F. Forstnerič, Analytic disks with boundaries in a maximal real submanifold of $ \mathbb{C}^2$, Ann. Inst. Fourier (Grenoble) 37, no. 1 (1987), 1-44. MR 0894560 (88j:32019)
  • 7. J. Garnett and D. Marshall, Harmonic Measure, Cambridge University Press, 2005. MR 2150803 (2006g:31002)
  • 8. P. Koosis, Introduction to $ H_{p}$ Spaces, second edition, Cambridge University Press, 1998. MR 1669574 (2000b:30052)
  • 9. T. Ransford, Potential Theory in the Complex Plane, Cambridge University Press, 1995. MR 1334766 (96e:31001)
  • 10. W. Rudin, Totally Real Klein Bottles in $ \mathbb{C}^2$, Proc. A.M.S. 82, no. 4 (1981), 653-654. MR 614897 (82i:32012)
  • 11. E. L. Stout, Polynomial Convexity, Prog. in Math. 261, Birkhäuser, 2007. MR 2305474 (2008d:32012)
  • 12. J. Wermer, Subharmonicity and Hulls, Pac. J. Math. 58, no. 1 (1975), 283-290. MR 0393567 (52:14376)

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Additional Information

John T. Anderson
Affiliation: Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, Massachusetts 01610
Email: anderson@mathcs.holycross.edu

DOI: https://doi.org/10.1090/S0002-9939-2011-10998-5
Keywords: Polynomial hull, Klein bottle
Received by editor(s): November 20, 2010
Published electronically: June 2, 2011
Communicated by: Franc Forstneric
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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