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A differentiable point of the distance function to the cut locus. (English) Zbl 1017.53040

In this note, the author announces a characterization of the points in the unit normal bundle of a closed submanifold \(N\) in a 2-dimensional complete Riemannian manifold \(M\) where the distance function \(\rho\) to the cut locus of \(N\) is differentiable. This result is motivated by a conjecture due to S. L. Kokkendorff, that was in turn inspired by the experimentation with the software tool “Loki”.

MSC:

53C22 Geodesics in global differential geometry

Software:

Loki
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