Rigidity in non-negative curvature
Cut and singular loci up to codimension 3
We give a new and detailed description of the structure of cut loci, with direct applications to the singular sets of some Hamilton-Jacobi equations. These sets may be non-triangulable, but a local description at all points except for a set of Hausdorff dimension is well known. We go further in this direction by giving a classification of all points up to a set of Hausdorff dimension .
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