A comparison of symplectic homogenization and Calabi quasi-states
Symplectic Geometry
2010-10-05 v2 Functional Analysis
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 while 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.
Keywords
Cite
@article{arxiv.1008.2449,
title = {A comparison of symplectic homogenization and Calabi quasi-states},
author = {Alexandra Monzner and Frol Zapolsky},
journal= {arXiv preprint arXiv:1008.2449},
year = {2010}
}
Comments
added a link to asymptotic Hofer geometry, 25 pages, 3 figures