A comparison of symplectic homogenization and Calabi quasi-states

Details A comparison of symplectic homogenization and Calabi quasi-states A comparison of symplectic homogenization and Calabi quasi-states

2010-08-14

arxiv.org/abs/1008.2449v2

Mathematics

Symplectic Geometry

added a link to asymptotic Hofer geometry, 25 pages, 3 figures

Scientific paper

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.

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