|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
On
certain quantifications of Gromov's nonsqueezing theorem
Kevin Sackel, Antoine Song, Umut Varolgunes and Jonathan J ZhuAppendix: Joé Brendel |
|
Geometry & Topology 28 (2024) 1113–1152
|
 |
Abstract |
|
Let and let be the Euclidean –ball of radius with a closed subset removed. Suppose that embeds symplectically into the unit cylinder . By Gromov’s nonsqueezing theorem, must be nonempty. We prove that the Minkowski dimension of is at least , and we exhibit an explicit example showing that this result is optimal at least for . In the appendix by Joé Brendel, it is shown that the lower bound is optimal for . We also discuss the minimum volume of in the case that the symplectic embedding extends, with bounded Lipschitz constant, to the entire ball. |
Keywords
Gromov nonsqueezing, waist inequality, folding
|
Mathematical Subject Classification
Primary: 53D05, 53D35
|
References |
Publication
Received: 22 May 2021
Revised: 5 April 2022
Accepted: 11 September 2022
Published: 10 May 2024
Proposed: Yakov Eliashberg
Seconded: Leonid Polterovich, Tobias H Colding
|
Authors |
| Kevin Sackel | |
| Department of Mathematics and
Statistics University of Massachusetts, Amherst Amherst, MA United States |
|
| Antoine Song | |
| Mathematics Department California Institute of Technology Pasadena, CA United States |
|
| Umut Varolgunes | |
| Department of Mathematics Boğaziçi University İstanbul Turkey |
|
| Jonathan J Zhu | |
| Department of Mathematics University of Washington Seattle, WA United States |
|
| Joé Brendel | |
| Institut de Mathématiques Université de Neuchâtel Neuchâtel Switzerland |
|
| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
Open Access made possible by participating institutions via Subscribe to Open.
