Hofer’s question on intermediate symplectic capacities
نویسنده
چکیده
Roughly twenty five years ago Hofer asked: can the cylinder B2(1)×R2(n−1) be symplectically embedded into B2(n−1)(R)×R2 for some R > 0? We show that this is the case if R > √ 2n−1 + 2n−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.
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