English

Discontinuous symplectic capacities

Symplectic Geometry 2014-05-13 v4

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.

Cite

@article{arxiv.1208.6000,
  title  = {Discontinuous symplectic capacities},
  author = {Kai Zehmisch and Fabian Ziltener},
  journal= {arXiv preprint arXiv:1208.6000},
  year   = {2014}
}

Comments

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

R2 v1 2026-06-21T21:56:59.920Z