• Corpus ID: 208006425

# Symplectic embeddings of the $\ell_p$-sum of two discs

@article{Ostrover2019SymplecticEO,
title={Symplectic embeddings of the \$\ell\_p\$-sum of two discs},
author={Yaron Ostrover and Vinicius G. B. Ramos},
journal={arXiv: Symplectic Geometry},
year={2019}
}
• Published 14 November 2019
• Mathematics
• arXiv: Symplectic Geometry
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 in these cases, and show how different kinds of embedding rigidity and flexibility phenomena appear as a function of the parameter $p$.
3 Citations

## Figures from this paper

Remarks on symplectic capacities of $p$-products
• Mathematics
• 2021
In this note we study the behavior of symplectic capacities of convex domains in the classical phase space with respect to symplectic p-products. As an application, by using a “tensor power trick”,
Towards the strong Viterbo conjecture
• Mathematics
• 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
The Viterbo's capacity conjectures for convex toric domains and the product of a $1$-unconditional convex body and its polar
• Mathematics
• 2020
In this note, we show that the strong Viterbo conjecture holds true on any convex toric domain, and that the Viterbo's volume-capacity conjecture holds for the product of a $1$-unconditional convex

## References

SHOWING 1-10 OF 22 REFERENCES
Symplectic embeddings and the lagrangian bidisk
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
On the rigidity of lagrangian products
• Mathematics
Journal of Symplectic Geometry
• 2019
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
Packing numbers of rational ruled four-manifolds
• Mathematics
• 2013
We completely solve the symplectic packing problem with equally sized balls for any rational, ruled, symplectic four-manifolds. We give explicit formulae for the packing numbers, the generalized
J-Holomorphic Curves and Symplectic Topology
• Mathematics
• 2004
The theory of $J$-holomorphic curves has been of great importance since its introduction by Gromov in 1985. In mathematics, its applications include many key results in symplectic topology. It was
Symplectic embeddings into four‐dimensional concave toric domains
• Mathematics
• 2013
ECH (embedded contact homology) capacities give obstructions to symplectically embedding one symplectic four‐manifold with boundary into another. We compute the ECH capacities of a large family of
Symplectic embeddings from concave toric domains into convex ones
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",
The Hofer conjecture on embedding symplectic ellipsoids
In this note we show that one open four dimensional ellipsoid embeds symplectically into another if and only the ECH capacities of the first are no larger than those of the second. This proves a
The embedding capacity of 4-dimensional symplectic ellipsoids
• Mathematics
• 2009
This paper calculates the function $c(a)$ whose value at $a$ is the infimum of the size of a ball that contains a symplectic image of the ellipsoid $E(1,a)$. (Here $a \ge 1$ is the ratio of the area
Symplectic genus, minimal genus and diffeomorphisms
• Mathematics
• 2001
In this paper, the symplectic genus for any 2-dimensional class in a 4-manifold admitting a symplectic structure is introduced, and its relation with the minimal genus is studied. It is used to
Symplectic embeddings of 4‐dimensional ellipsoids
We show how to reduce the problem of symplectically embedding one 4-dimensional rational ellipsoid into another to a problem of embedding disjoint unions of balls into ℂP 2 . For example, the problem