In this paper a sequence of convex sets of increasing dimension is constructed for which the Ekeland-Hofer-Zehnder capacity is uniformly bounded while the symplectic capacity grows to infinity. This contrasts sharply with the recent result from the paper by E. D. Gluskin, Y. Ostrover, Comm. Math. Helv. 91 (2016), no. 1, 131-144, which shows that there are no such examples in the case of centrally symmetric convex bodies.
- Asymptotic theory of finite dimensional spaces
- Convex bodies
- Symplectic capacity