Relevant bibliographies by topics / Conjecture de Viterbo

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters

Academic literature on the topic 'Conjecture de Viterbo'

Author: Grafiati
Published: 2 November 2024
Last updated: 31 July 2025

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Journal articles on the topic "Conjecture de Viterbo"

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Abbondandolo, Alberto, Barney Bramham, Umberto L. Hryniewicz, and Pedro A. S. Salomão. "Systolic ratio, index of closed orbits and convexity for tight contact forms on the three-sphere." Compositio Mathematica 154, no. 12 (2018): 2643–80. http://dx.doi.org/10.1112/s0010437x18007558.

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We construct a dynamically convex contact form on the three-sphere whose systolic ratio is arbitrarily close to 2. This example is related to a conjecture of Viterbo, whose validity would imply that the systolic ratio of a convex contact form does not exceed 1. We also construct, for every integer $n\geqslant 2$, a tight contact form with systolic ratio arbitrarily close to $n$ and with suitable bounds on the mean rotation number of all the closed orbits of the induced Reeb flow.
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Balitskiy, Alexey. "Equality Cases in Viterbo’s Conjecture and Isoperimetric Billiard Inequalities." International Mathematics Research Notices 2020, no. 7 (2018): 1957–78. http://dx.doi.org/10.1093/imrn/rny076.

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Abstract We apply the billiard technique to deduce some results on Viterbo’s conjectured inequality between the volume of a convex body and its symplectic capacity. We show that the product of a permutohedron and a simplex (properly related to each other) delivers equality in Viterbo’s conjecture. Using this result as well as previously known equality cases, we prove some special cases of Viterbo’s conjecture and interpret them as isoperimetric-like inequalities for billiard trajectories.
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Karasev, Roman, and Anastasia Sharipova. "Viterbo’s Conjecture for Certain Hamiltonians in Classical Mechanics." Arnold Mathematical Journal 5, no. 4 (2019): 483–500. http://dx.doi.org/10.1007/s40598-019-00129-4.

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Valverde-Albacete, Francisco J., and Carmen Peláez-Moreno. "The Rényi Entropies Operate in Positive Semifields." Entropy 21, no. 8 (2019): 780. http://dx.doi.org/10.3390/e21080780.

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We set out to demonstrate that the Rényi entropies are better thought of as operating in a type of non-linear semiring called a positive semifield. We show how the Rényi’s postulates lead to Pap’s g-calculus where the functions carrying out the domain transformation are Rényi’s information function and its inverse. In its turn, Pap’s g-calculus under Rényi’s information function transforms the set of positive reals into a family of semirings where “standard” product has been transformed into sum and “standard” sum into a power-emphasized sum. Consequently, the transformed product has an invers
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Gutt, Jean, Michael Hutchings, and Vinicius G. B. Ramos. "Examples around the strong Viterbo conjecture." Journal of Fixed Point Theory and Applications 24, no. 2 (2022). http://dx.doi.org/10.1007/s11784-022-00949-6.

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Shelukhin, Egor. "Viterbo conjecture for Zoll symmetric spaces." Inventiones mathematicae, July 7, 2022. http://dx.doi.org/10.1007/s00222-022-01124-x.

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7

Shelukhin, Egor. "Symplectic cohomology and a conjecture of Viterbo." Geometric and Functional Analysis, October 31, 2022. http://dx.doi.org/10.1007/s00039-022-00619-2.

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Edtmair, O. "Disk-Like Surfaces of Section and Symplectic Capacities." Geometric and Functional Analysis, July 16, 2024. http://dx.doi.org/10.1007/s00039-024-00689-4.

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AbstractWe prove that the cylindrical capacity of a dynamically convex domain in ${\mathbb{R}}^{4}$ agrees with the least symplectic area of a disk-like global surface of section of the Reeb flow on the boundary of the domain. Moreover, we prove the strong Viterbo conjecture for all convex domains in ${\mathbb{R}}^{4}$ which are sufficiently C3 close to the round ball. This generalizes a result of Abbondandolo-Bramham-Hryniewicz-Salomão establishing a systolic inequality for such domains.
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Abbondandolo, Alberto, and Gabriele Benedetti. "On the local systolic optimality of Zoll contact forms." Geometric and Functional Analysis, February 3, 2023. http://dx.doi.org/10.1007/s00039-023-00624-z.

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AbstractWe prove a normal form for contact forms close to a Zoll one and deduce that Zoll contact forms on any closed manifold are local maximizers of the systolic ratio. Corollaries of this result are: (1) sharp local systolic inequalities for Riemannian and Finsler metrics close to Zoll ones, (2) the perturbative case of a conjecture of Viterbo on the symplectic capacity of convex bodies, (3) a generalization of Gromov’s non-squeezing theorem in the intermediate dimensions for symplectomorphisms that are close to linear ones.
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Rudolf, Daniel. "Viterbo’s conjecture as a worm problem." Monatshefte für Mathematik, December 18, 2022. http://dx.doi.org/10.1007/s00605-022-01806-x.

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AbstractIn this paper, we relate Viterbo’s conjecture from symplectic geometry to Minkowski versions of worm problems which are inspired by the well-known Moser worm problem from geometry. For the special case of Lagrangian products this relation provides a connection to systolic Minkowski billiard inequalities and Mahler’s conjecture from convex geometry. Moreover, we use the above relation in order to transfer Viterbo’s conjecture to a conjecture for the longstanding open Wetzel problem which also can be expressed as a systolic Euclidean billiard inequality and for which we discuss an algori
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Dissertations / Theses on the topic "Conjecture de Viterbo"

1

Dardennes, Julien. "Non-convexité symplectique des domaines toriques." Electronic Thesis or Diss., Université de Toulouse (2023-....), 2024. http://www.theses.fr/2024TLSES102.

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La convexité joue un rôle particulier en géométrie symplectique, pourtant ce n'est pas une notion invariante par symplectomorphisme. Dans un article fondateur, Hofer, Wysocki et Zehnder ont montré que tout domaine fortement convexe est dynamiquement convexe, une notion, qui elle, est invariante par symplectomorphisme. Depuis plus de vingt ans, l'existence ou non de domaines dynamiquement convexes qui ne sont pas symplectomorphes à un convexe est restée une question ouverte. Récemment, Chaidez et Edtmair ont répondu à cette question en dimension 4. Ils ont établi un critère "quantitatif" de con
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Book chapters on the topic "Conjecture de Viterbo"

1

Hofer, Helmut, Alberto Abbondandolo, Urs Frauenfelder, and Felix Schlenk. "Examples around the strong Viterbo conjecture." In Symplectic Geometry. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-19111-4_22.

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2

Ekeland, Ivar. "Viterbo’s Proof of Weinstein’s Conjecture in R 2n." In Periodic Solutions of Hamiltonian Systems and Related Topics. Springer Netherlands, 1987. http://dx.doi.org/10.1007/978-94-009-3933-2_11.

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