Metric and isoperimetric problems in symplectic geometry

By C. Viterbo. 2000

127 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d8b1abc217e2692e51da75bf63f5d65c447a238f

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Quantitative symplectic geometry (2005, unknown): “Using John’s ellipsoid, Viterbo [100] noticed that there is a constant Cn depending only on n such that c(U) ≤ Cn cB(U) for all U ∈ Conv and so, in view of (8), cB(U) ≤ c(U) ≤ Cn c(Z) cB(U) for all U ∈ Conv .”
Symplectic capacities from positive S1–equivariant symplectic homology (2017, background): “n also consider normalized symplectic capacities, which satisfy the additional properties cpBp1qqcpZp1qq1, where we dene the cylinder ZpaqPpa;8;:::;8q. A strong version of a conjecture of Viterbo [Vit00] asserts that all normalized symplectic capacities agree on compact convex domains in R2n. For ex”
Contact geometry and isosystolic inequalities (2011, background): “ngent plane to ∂K at the point ζ(t). In other words, if hK : S2n−1 → R is the support function of K, the action of the closed characteristic ζ is the integral Action(ζ) := 1 2 ZT 0 hK(n(ζ(t)))dt . In [30] C. Viterbo asked whether the ball in Cn has the largest symplectic capacity among all convex bo”
The Restricted Three-Body Problem and Holomorphic Curves (2018, result): “Indeed, it is known that in the convex case the Hofer-Zehnder capacity coincides with the systole [130], and obtaining estimates for the systole in the convex case is strongly related to the famous Viterbo conjecture [236, 198].”
Hamiltonian stationary Lagrangian surfaces in C^2 (2000, background): “Viterbo [V], who also gave a lower bound for the area functional of a torus.”
Erratum to “Geometry of contact transformations and domains: orderability versus squeezing” (2005, background): “For instance, all convex domains lie in „D for D D 4n (see [46],[11]).”
From symplectic measurements to the Mahler conjecture (2013, background): “This theorem improves a previous result of Viterbo in [29], where inequality (1.”
Embedding Problems in Symplectic Geometry (2005, background): “It is conjectured that this holds for any bounded convex domain [36].”
The "M"-ellipsoid, symplectic capacities and volume (2006, methodology): “In [20], Viterbo investigated the relation between the classical Riemannian way of measuring the size of sets using the canonical volume and the symplectic way using symplectic capacities.”
Existence and non-existence of solutions for a class of Monge–Ampère equations (2009, background): “John (see [1] or [12]) says that there exists an ellipsoid P such that P ⊂Ω ⊂ nP .”