Viterbo’s conjecture as a worm problem

Monatshefte für Mathematik, vol. 201, pp. 217–287

Abstract

Abstract In 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.

Authors 1

1. Daniel Rudolf corresponding Aachen Lehrstuhl für Geometrie und Analysis

   RWTH Aachen University

   Affiliation as printed

   Lehrstuhl für Geometrie und Analysis, RWTH Aachen, Pontdriesch 10-12, 52062, Aachen, Deutschland

   Lehrstuhl für Geometrie und Analysis, RWTH Aachen, Aachen, Deutschland