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Length maximizing invariant measures in Lorentzian geometry

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Suhr, Stefan
Date of publication of this fulltext: 18 Apr 2011 06:52


We introduce a version of Aubry-Mather theory for the length functional of causal curves in a compact Lorentzian manifold. Results include the existence of maximal invariant measures, calibrations and calibrated curves. We prove two versions of Mather’s graph theorem for Lorentzian manifolds. A class of examples (Lorentzian Hedlund examples) shows the optimality of the results.

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