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Title:
From curves to currents
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Abstract:
Bonahon introduced the space of geodesic currents, a space that contains all closed weighted closed curves as a dense subspace (generalizing measured laminations, which contain weighted simple closed curves). We give a simple criterion for when a function on weighted curves extends to a continuous function on geodesic currents; the key restriction is that it is monotone under smoothing a crossing. This puts all known results of functions extending to geodesic currents in a unified framework.
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