TY - JOUR
T1 - Lagrangian caps
AU - Eliashberg, Yakov
AU - Murphy, Emmy
N1 - Funding Information:
Yakov Eliashberg was Partially supported by the NSF grant DMS-1205349. Emmy Murphy was Partially supported by the NSF grant DMS-0943787.
PY - 2013/10
Y1 - 2013/10
N2 - 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 ℝ2n, 2n ≥ 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).
AB - 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 ℝ2n, 2n ≥ 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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U2 - 10.1007/s00039-013-0239-2
DO - 10.1007/s00039-013-0239-2
M3 - Article
AN - SCOPUS:84884411224
SN - 1016-443X
VL - 23
SP - 1483
EP - 1514
JO - Geometric and Functional Analysis
JF - Geometric and Functional Analysis
IS - 5
ER -