Squeezing Lagrangian tori in dimension 4

  • Richard Hind

    University of Notre Dame, USA
  • Emmanuel Opshtein

    Université de Strasbourg, France
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Let C2\mathbb C^2 be the standard symplectic vector space and L(a,b)C2L(a,b) \subset \mathbb C^2 be the product Lagrangian torus, that is, a product of two circles of areas aa and bb in C\mathbb C. We give a complete answer to the question of finding the minimal ball into which these Lagrangians may be squeezed by a Hamiltonian flow. The result is that there is full rigidity when ab2aa \leq b \leq 2a, which disappears almost completely when b>2ab > 2a.

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Richard Hind, Emmanuel Opshtein, Squeezing Lagrangian tori in dimension 4. Comment. Math. Helv. 95 (2020), no. 3, pp. 535–567

DOI 10.4171/CMH/496