Length Maximizing Invariant Measures in Lorentzian Geometry

Details Length Maximizing Invariant Measures in Lorentzian Geometry Length Maximizing Invariant Measures in Lorentzian Geometry

Publishing date

2011-02-07

URL

arxiv.org/abs/1102.1386v1

Science

Mathematics

Field

Differential Geometry

Additional info

41 pages

Type

Scientific paper

Abstract

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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