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Journal Articles Mathematical Proceedings of the Cambridge Philosophical Society Year : 2011

On smooth time functions

Abstract

We are concerned with the existence of smooth time functions on connected time{oriented Lorentzian manifolds. The problem is tackled in a more general abstract setting, namely in a manifold M where is just de ned a eld of tangent convex cones (Cx)x2M enjoying mild continuity properties. Under some conditions on its integral curves, we will construct a time function. Our approach is based on the de nition of an intrinsic length for curves indicating how a curve is far from being an integral trajectory of Cx. We nd connections with topics pertaining to Hamilton{Jacobi equations, and make use of tools and results issued from weak KAM theory.
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Dates and versions

hal-00660452 , version 1 (16-01-2012)

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Albert Fathi, Antonio Siconolfi. On smooth time functions. Mathematical Proceedings of the Cambridge Philosophical Society, 2011, ⟨10.1017/S0305004111000661⟩. ⟨hal-00660452⟩
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