Translator Disclaimer
15 June 2017 Symplectic embeddings and the Lagrangian bidisk
Vinicius Gripp Barros Ramos
Duke Math. J. 166(9): 1703-1738 (15 June 2017). DOI: 10.1215/00127094-0000011X

Abstract

In this article we obtain sharp obstructions to the symplectic embedding of the Lagrangian bidisk into four-dimensional balls, ellipsoids, and symplectic polydisks. We prove, in fact, that the interior of the Lagrangian bidisk is symplectomorphic to a concave toric domain by using ideas that come from billiards on a round disk. In particular, we answer a question of Ostrover. We also obtain sharp obstructions to some embeddings of ellipsoids into the Lagrangian bidisk.

Citation

Download Citation

Vinicius Gripp Barros Ramos. "Symplectic embeddings and the Lagrangian bidisk." Duke Math. J. 166 (9) 1703 - 1738, 15 June 2017. https://doi.org/10.1215/00127094-0000011X

Information

Received: 28 September 2015; Revised: 25 October 2016; Published: 15 June 2017
First available in Project Euclid: 2 March 2017

zbMATH: 1370.53057
MathSciNet: MR3662442
Digital Object Identifier: 10.1215/00127094-0000011X

Subjects:
Primary: 53D05
Secondary: 53D42

Keywords: Billiards , concave toric domains , embedded contact homology capacities , Lagrangian bidisk , symplectic embeddings

Rights: Copyright © 2017 Duke University Press

JOURNAL ARTICLE
36 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.166 • No. 9 • 15 June 2017
Back to Top