Lagrangian caps
By Y. Eliashberg, Emmy Murphy. Geometric and Functional Analysis, 2013
63 citations recorded by the source corpus.
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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}^{2n}, 2n \geq 6}$$\end{document}, 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).
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/fb1da7a25f0e6d5ff1c707947d3bfdc0d4e659d2
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Geometry and Topology
- Roger Casals
- Emmy Murphy
- Y. Eliashberg
- A. Stipsicz
- P. Ghiggini
- Michael Hutchings
- John B. Etnyre
- P. Lisca
Citations in the corpus
- Making cobordisms symplectic (2015, background): “4, with a similar flexibility phenomenon for Lagrangian manifolds with conical singularities with loose Legendrian links, which was uncovered in [7].”
- Legendrian fronts for affine varieties (2016, background): “Finally we remark that all of these questions are known to have counterexamples if we allow either Lagrangians with concave boundary inside the boundary of a Darboux ball, or closed Lagrangians inside Weinstein cobordisms with nonempty concave contact boundary [32].”