Roughly twenty five years ago Hofer asked: can the cylinder B^2(1) \times \mathbb{ R}^{ 2(n-1)} be symplectically embedded into B^{ 2(n-1)}(R) \times \mathbb{ R}^2 for some R>0? We show that this is the case if R \geq \sqrt{ 2^{ n-1}+2^{ n-2}-2}. We deduce that there are no intermediate capacities, between 1-capacities, first constructed by Gromov in 1985, and n-capacities, answering another question of Hofer. In 2008, Guth reached the same conclusion under the additional hypothesis that the intermediate capacities should satisfy the exhaustion property.
Categories: math.SG math.DS