Symplectic embeddings of polydisks

• R. Hind ^[1] ; S. Lisi ^[2]
  1. [1] University of Notre Dame

     University of Notre Dame

     Township of Portage, Estados Unidos

     
  2. [2] University of Nantes

     University of Nantes

     Arrondissement de Nantes, Francia

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 21, Nº. 3, 2015, págs. 1099-1120
• Idioma: inglés
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• Resumen

  • We show that the polydisk P(1,2)P(1,2) , the product of disks of areas 11 and 22 , can be symplectically embedded in a ball B(R)B(R) of capacity RR if and only if R≥3R≥3 . Hence, the inclusion map gives the optimal embedding and neither the Embedded Contact Homology nor Ekeland–Hofer capacities give sharp obstructions in this situation. Our proof applies the theory of pseudoholomorphic curves in manifolds with cylindrical ends, and in particular finite energy foliations.