Non-squeezing property of contact balls

Abstract

In this paper we solve a contact non-squeezing conjecture proposed by Eliashberg, Kim and Polterovich. Let $B_R$ be the open ball of radius $R$ in ${\mathbf{R}}^{2n}$ and let ${\mathbf{R}}^{2n}\times {\mathbf{S}}^1$ be the prequantization space equipped with the standard contact structure. Following Tamarkin's idea, we apply microlocal category methods to prove that if $R$ and $r$ satisfy $1\le \pi r^2<\pi R^2$, then it is impossible to squeeze the contact ball $B_R\times {\mathbf{S}}^1$ into $B_r\times {\mathbf{S}}^1$ via compactly supported contact isotopies.

38 pages

References in corpus (5)

• Legendrian knots and constructible sheaves
• Cluster varieties from Legendrian knots
• Microlocal condition for non-displaceablility
• The Gromov-Eliashberg theorem by microlocal sheaf theory
• Contact non-squeezing at large scale in ${\mathbb{R}}^{2n}\times S^1$

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• Hamiltonian perturbations in contact Floer homology
• Selective symplectic homology with applications to contact non-squeezing
• Contact non-squeezing at large scale in ${\mathbb{R}}^{2n}\times S^1$
• Geometry and analysis of contact instantons and entanglement of Legendrian links I
• Radon Transform for Sheaves
• Relative growth rate and contact Banach-Mazur distance
• Estimating Reeb chords using microlocal sheaf theory
• Microlocal Projector for Complete Flow