Some Consequences of the Nature of the Distance Function on the Cut Locus in a Riemannian Manifold
D. Barden, Huiling Le · Journal of the London Mathematical Society · 1997
We render the cut locus more accessible to analysis by showing that each non-conjugate cut point has a neighbourhood on which the distance function is the minimum of finitely many smooth ‘radial functions’. This enables us to generalise to an arbitrary complete manifold a number of recent results, mainly from stochastic analysis, which were either limited or not valid on the cut locus because of the lack of differentiability there of the distance function.