Lagrangian caps

Yakov Eliashberg; Emmy Murphy

doi:10.1007/s00039-013-0239-2

Lagrangian caps

Yakov Eliashberg^*, Emmy Murphy

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

42 Scopus citations

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 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).

Original language	English (US)
Pages (from-to)	1483-1514
Number of pages	32
Journal	Geometric and Functional Analysis
Volume	23
Issue number	5
DOIs	https://doi.org/10.1007/s00039-013-0239-2
State	Published - Oct 2013

Funding

Yakov Eliashberg was Partially supported by the NSF grant DMS-1205349. Emmy Murphy was Partially supported by the NSF grant DMS-0943787.

ASJC Scopus subject areas

Analysis
Geometry and Topology

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10.1007/s00039-013-0239-2

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title = "Lagrangian caps",

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 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).",

author = "Yakov Eliashberg and Emmy Murphy",

note = "Funding Information: Yakov Eliashberg was Partially supported by the NSF grant DMS-1205349. Emmy Murphy was Partially supported by the NSF grant DMS-0943787.",

year = "2013",

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doi = "10.1007/s00039-013-0239-2",

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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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JF - Geometric and Functional Analysis

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ER -

Lagrangian caps

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ASJC Scopus subject areas

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