Averaging sequences
Fernando Alcalde Cuesta, Ana Rechtman
TL;DR
This paper introduces an averaging condition for foliations that helps identify tangentially smooth measures with specific Radon-Nikodym cocycles, extending the understanding of harmonic measures.
Contribution
It proposes a new averaging condition for foliations to find tangentially smooth measures with prescribed cocycles, and provides conditions under which these are harmonic.
Findings
A new averaging condition for foliations is established.
Conditions are given for tangentially smooth measures to be harmonic.
Harmonic measures are shown as examples of tangentially smooth measures.
Abstract
In the spirit of Goodman-Plante average condition for the existence of a transverse invariant measure for foliations, we give an averaging condition to find tangentially smooth measures with prescribed Radon-Nikodym cocycle. Harmonic measures are examples of tangentially smooth measures for foliations and laminations. We also present sufficient hypothesis on the averaging condition under which the tangentially smooth measure is harmonic.
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