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Mathematische Annalen

, Volume 332, Issue 1, pp 55–65 | Cite as

Smooth submanifolds intersecting any analytic curve in a discrete set

  • Dan Coman
  • Norman Levenberg
  • Evgeny A. PoletskyEmail author
Article

Abstract.

We construct examples of C smooth submanifolds in ℂn and ℝn of codimension 2 and 1, which intersect every complex, respectively real, analytic curve in a discrete set. The examples are realized either as compact tori or as properly imbedded Euclidean spaces, and are the graphs of quasianalytic functions. In the complex case, these submanifolds contain real n-dimensional tori or Euclidean spaces that are not pluripolar while the intersection with any complex analytic disk is polar.

Keywords

Euclidean Space Analytic Curve Complex Case Smooth Submanifolds Analytic Disk 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Dan Coman
    • 1
  • Norman Levenberg
    • 2
  • Evgeny A. Poletsky
    • 1
    Email author
  1. 1.Department of MathematicsSyracuse UniversitySyracuseUSA
  2. 2.Department of MathematicsIndiana UniversityBloomingtonUSA

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