Ergodic invariant measure on the space of geodesic currents

Viveka Erlandsson, Gabriele Mondello

Research output: Contribution to journalArticle (Academic Journal)peer-review

Abstract

Let S be a compact, connected, oriented surface, possibly with boundary,
of negative Euler characteristic. In this article we extend Lindenstrauss-Mirzakhani’s
and Hamenst¨adt’s classification of (homogeneous and non-homogenous) locally finite mapping class group invariant ergodic measures on the space of measured laminations ML(S) to the space of geodesic currents C(S). Moreover, we also extend Lindenstrauss-Mirzakhani’s classification of orbit closures toC(S). Our argument relies on their results and on the decomposition of a current into a sum of three currents with isotopically disjoint supports: a measured lamination without closed leaves, a simple multi-curve and a current that binds its hull.
Original languageEnglish
Number of pages42
JournalAnnales de l'institut Fourier
Publication statusSubmitted - 2020

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