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Inventiones mathematicae

, Volume 203, Issue 1, pp 333–358 | Cite as

Rationally convex domains and singular Lagrangian surfaces in \(\mathbb {C}^2\)

  • Stefan Nemirovski
  • Kyler Siegel
Article

Abstract

We give a complete characterization of those disk bundles over surfaces which embed as rationally convex strictly pseudoconvex domains in \(\mathbb {C}^2\). We recall some classical obstructions and prove some deeper ones related to symplectic and contact topology. We explain the close connection to Lagrangian surfaces with isolated singularities and develop techniques for constructing such surfaces. Our proof also gives a complete characterization of Lagrangian surfaces with open Whitney umbrellas, answering a question first posed by Givental in 1986.

Keywords

Contact Structure Pseudoconvex Domain Klein Bottle Lagrangian Surface Lagrangian Torus 
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.

Notes

Acknowledgments

We would like to thank Yasha Eliashberg for suggesting this problem and for numerous informative discussions. We also thank Roger Casals and Emmy Murphy for enlightening conversations regarding Sect. 5.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteMoscowRussia
  2. 2.Fakultät für MathematikRuhr-Universität BochumBochumGermany
  3. 3.Department of MathematicsStanford UniversityStanfordUSA

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