Discontinuous symplectic capacities

Abstract

We show that the spherical capacity is discontinuous on a smooth family of ellipsoidal shells. Moreover, we prove that the shell capacity is discontinuous on a family of open sets with smooth connected boundaries.

We include generalizations to higher dimensions due to the unknown referee and Janko Latschev. We add examples of open sets with connected boundary on which the shell capacity is not continuous. 3rd and 4th version: minor changes, to appear in J. Fixed Point Theory Appl

References in corpus (2)

• How to recognise a 4-ball when you see one
• Symplectic cobordisms and the strong Weinstein conjecture

Cited by in corpus (2)

• Polyfolds, Cobordisms, and the strong Weinstein conjecture
• Lagrangian non-squeezing and a geometric inequality