Regularity of the geodesic flow on submanifolds

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Christian Lange This is my paper · ORCID

classification math.DGmath.MG

keywords flowgeodesicclassexponentialmathbbregularitysubmanifoldsubmanifolds

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abstract

We show that the geodesic flow and the exponential map of a $C^k$ submanifold of $\mathbb{R}^n$ with $k\geq 2$ are of class $C^{k-1}$.

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Non-persistence of strongly isolated singularities, and geometric applications
math.DG 2024-11 accept novelty 8.0 of 10

For generic metrics, stationary varifolds with only strongly isolated singularities either are smooth or have a more complicated singularity; in codimension one, only smooth or non-strongly-isolated objects persist.