# Symplectic embeddings and the lagrangian bidisk

@article{Ramos2017SymplecticEA, title={Symplectic embeddings and the lagrangian bidisk}, author={Vinicius G. B. Ramos}, journal={Duke Mathematical Journal}, year={2017}, volume={166}, pages={1703-1738} }

In this paper 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 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.

## 11 Citations

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- 2021

In this paper, we compute the embedded contact homology (ECH) capacities of the disk cotangent bundles D∗S2 and D∗RP 2. We also find sharp symplectic embeddings into these domains. In particular, we…

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Motivated by work of the first author, this paper studies symplectic embedding problems of lagrangian products that are sufficiently symmetric. In general, lagrangian products arise naturally in the…

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Embedded contact homology gives a sequence of obstructions to four-dimensional symplectic embeddings, called ECH capacities. In "Symplectic embeddings into four-dimensional concave toric domains",…

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In this paper we study symplectic embedding questions for the $\ell_p$-sum of two discs in ${\mathbb R}^4$, when $1 \leq p \leq \infty$. In particular, we compute the symplectic inner and outer radii…

On the Ekeland–Hofer symplectic capacities of
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In $\mathbb{C}^2$ with the standard symplectic structure we consider the bidisc $D^2\times D^2$ constructed as the product of two open real discs of radius $1$. We compute explicit values for the…

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In this paper we settle three basic questions concerning the Gutt-Hutchings capacities from [9] which are conjecturally equal to the Ekeland-Hofer capacities from [7, 8]. Our primary result settles a…

Towards the strong Viterbo conjecture

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- 2020

This paper is a step towards the strong Viterbo conjecture on the coincidence of all symplectic capacities on convex domains. Our main result is a proof of this conjecture in dimension 4 for the…

Examples around the strong Viterbo conjecture

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A strong version of a conjecture of Viterbo asserts that all normalized symplectic capacities agree on convex domains. We review known results showing that certain specific normalized symplectic…

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