A comparison of symplectic homogenization and Calabi quasi-states

2010/08/14 by Monzner, Alexandra, Zapolsky, Frol · 1 citation
#53D99 #58C35 #FOS: Mathematics #Functional Analysis (math.FA) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1008.2449

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^*S¹. Proofs are based on the theory of quasi-integrals and topological measures on locally compact spaces.

Cited by

• Hofer-continuous quasi-morphisms on Liouville manifolds

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