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Lagrangian caps

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Abstract

We establish an h-principle for exact Lagrangian embeddings with concave Legendrian boundary. We prove, in particular, that in the complement of the unit ball B in the standard symplectic \({\mathbb{R}^{2n}, 2n \geq 6}\), there exists an embedded Lagrangian n-disc transversely attached to B along its Legendrian boundary, which is loose in the sense of Murphy (Loose Legendrian embeddings in high dimensional contact manifolds, arXiv:1201.2245, 2013).

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Authors and Affiliations

  1. Department of Mathematics, Stanford University, 450 Serra Mall, Stanford, CA, 94305, USA

    Yakov Eliashberg

  2. Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139-4307, USA

    Emmy Murphy

Authors
  1. Yakov Eliashberg
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  2. Emmy Murphy
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Corresponding author

Correspondence to Yakov Eliashberg.

Additional information

Yakov Eliashberg was Partially supported by the NSF grant DMS-1205349.

Emmy Murphy was Partially supported by the NSF grant DMS-0943787.

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Eliashberg, Y., Murphy, E. Lagrangian caps. Geom. Funct. Anal. 23, 1483–1514 (2013). https://doi.org/10.1007/s00039-013-0239-2

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  • DOI: https://doi.org/10.1007/s00039-013-0239-2

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