Abstract
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 algorithmic approach in order to find a new lower bound. Finally, we point out that the above mentioned relation between Viterbo’s conjecture and Minkowski worm problems has a structural similarity to the known relationship between Bellmann’s lost-in-a-forest problem and the original Moser worm problem.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Reference55 articles.
1. Abbondandolo, A., Majer, P.: A non-squeezing theorem for convex symplectic images of the Hilbert ball. Calc. Var. Partial Differ. Equ. 54, 1469–1506 (2015)
2. Akopyan, A., Karasev, R.: Estimating symplectic capacities from lengths of closed curves on the unit spheres. arXiv:1801.00242 (2017)
3. Artstein-Avidan, S., Karasev, R., Ostrover, Y.: From symplectic measurements to the Mahler conjecture. Duke Math. J. 163(11), 2003–2022 (2014)
4. Balitskiy, A.: Equality cases in viterbo’s conjecture and isoperimetric billiard inequalities. Int. Math. Res. Not. 2020(7), 1957–1978 (2020)
5. Bellman, R.: Minimization problem. Bull. Am. Math. Soc. 62, 270 (1956)
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