• Corpus ID: 214623119

Towards the strong Viterbo conjecture

@article{Gutt2020TowardsTS,
  title={Towards the strong Viterbo conjecture},
  author={Jean Gutt and Vinicius G. B. Ramos},
  journal={arXiv: Symplectic Geometry},
  year={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 classes of convex and concave toric domains. The second result is that, in any dimension, $c_{1}^{\operatorname{Ekeland-Hofer}}(W)=c_1^{CH}(W)=c_{\operatorname{Viterbo}}(W)$ for all convex domains $W\subset\mathbb{R}^{2n}$. Moreover, if $W$ is a convex or concave toric domain $W=X_\Omega\subset\mathbb{R… 
2 Citations
Quantum Polar Duality and the Symplectic Camel: A New Geometric Approach to Quantization
TLDR
It is shown that the orthogonal projections of the covariance ellipsoid of a quantum state on the configuration and momentum spaces form what the authors call a dual quantum pair, which allows solving the Pauli reconstruction problem for Gaussian wavefunctions.
The Viterbo's capacity conjectures for convex toric domains and the product of a $1$-unconditional convex body and its polar
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 24 REFERENCES
Symplectic capacities from positive S1–equivariant symplectic homology
We use positive S^1-equivariant symplectic homology to define a sequence of symplectic capacities c_k for star-shaped domains in R^{2n}. These capacities are conjecturally equal to the Ekeland-Hofer
Functors and Computations in Floer Homology with Applications, I
Abstract. This paper is concerned with Floer cohomology of manifolds with contact type boundary. In this case, there is no conjecture on this ring, as opposed to the compact case, where it is
Symplectic embeddings of the $\ell_p$-sum of two discs
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
Symplectic homology of convex domains and Clarke’s duality
We prove that the Floer complex that is associated with a convex Hamiltonian function on $\mathbb{R}^{2n}$ is isomorphic to the Morse complex of Clarke's dual action functional that is associated
From symplectic measurements to the Mahler conjecture
In this note we link symplectic and convex geometry by relating two seemingly different open conjectures: a symplectic isoperimetric-type inequality for convex domains, and Mahler's conjecture on the
Quantitative embedded contact homology
Define a "Liouville domain" to be a compact exact symplectic manifold with contact-type boundary. We use embedded contact homology to assign to each four-dimensional Liouville domain (or subset
Symplectic embeddings into four‐dimensional concave toric domains
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 Gysin exact sequence for $S^1$-equivariant symplectic homology
We define $S^1$-equivariant symplectic homology for symplectically aspherical manifolds with contact boundary, using a Floer-type construction first proposed by Viterbo. We show that it is related to
...
1
2
3
...