Regularity of geodesics in sets of positive reach
The main result of the paper states that if \(S\) is a regular positive reach set in \(\mathbb{R}^{n}\), then every geodesic in \(S\) (i.e., a locally shortest curve in \(S\)) is differentiable and its derivative is Lipschitz continuous.
scientific article; zbMATH DE number 6632092