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MGR Programmatic Seminar: On construction of time functions. October 31, 2013 (01:30 PM PDT - 02:30 PM PDT)
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Location: MSRI: Simons Auditorium
Speaker(s) Albert Fathi (Georgia Institute of Technology; École Normale Supérieure de Lyon)
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This is a joint work with Antonio Siconolfi. The purpose of this lecture is to introduce a different way to obtain Lipschitz time functions on causal Lorentzian manifolds. We will show that they can be obtained from a kind of degenerate auxiliary Finsler metric. We will also explain how this leads to the existence of smooth time functions. A feature of this approach is that it works more generally for fields of cones on a manifold. Our approach evolved from our work on smooth sub-solutions of the Hamilton-Jacobi Equation and the relevance of the Aubry set to this problem. However no prior knowledge of this last subject will be used in the lecture.

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