A Hausdorff-type metric is placed on the space of Cauchy hypersurfaces in globally hyperbolic spacetimes, yielding completeness and local compactness results that generalize earlier work by Beem and Takahashi.
Monclair, The Riemannian geometry of the space of compact spacelike Cauchy hypersurfaces, Preprint (2023)
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Hausdorff-type metric geometry of the space of Cauchy hypersurfaces
A Hausdorff-type metric is placed on the space of Cauchy hypersurfaces in globally hyperbolic spacetimes, yielding completeness and local compactness results that generalize earlier work by Beem and Takahashi.