In globally hyperbolic spacetimes, the locus of multiple maximizing geodesics is locally contractible and homotopy equivalent to the causal future minus the Lorentzian Aubry set.
The weak Kam theorem in Lagrangian dynamics
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On the locus of multiple maximizing geodesics on a globally hyperbolic spacetime
In globally hyperbolic spacetimes, the locus of multiple maximizing geodesics is locally contractible and homotopy equivalent to the causal future minus the Lorentzian Aubry set.