A comparison of symplectic homogenization and Calabi quasi-states
Loading...
Date
2011-02-11
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
We compare two functionals defined on the space of continuous functions
with compact support in an open neighborhood of the zero section
of the cotangent bundle of a torus. One comes from Viterbo's symplectic
homogenization, the other from the Calabi quasi-states due to Entov and
Polterovich. In dimension 2 we are able to say when these two functionals
are equal. A partial result in higher dimensions is presented. We also
give a link to asymptotic Hofer geometry on T^*S^1. Proofs are based on
the theory of quasi-integrals and topological measures on locally compact
spaces.