A Morse-Sard theorem for the distance function on Riemannian manifolds

61 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Semiconcavity results for optimal control problems admitting no singular minimizing controls (2008, background): “Such an approach leads to further regularity results, see [21] and [22].”
On Viscosity Solutions of Certain Hamilton–Jacobi Equations: Regularity Results and Generalized Sard's Theorems (2008, methodology): “Generalized Sard’s theorems have been recently used in [29], [39] and [40] to obtain regularity results on the level sets of distance functions in Riemannian and sub-Riemannian geometry.”
A nonsmooth Morse–Sard theorem for subanalytic functions (2006, background): “Existing deep results restrict attention to particular subclasses of functions (semialgebraic or “o-minimal,” for example) [3,6,10], distance functions to a manifold [17], or nonsmooth functions admitting a supremum representation [22], in order to relax the smoothness condition into simple differen”
A Comprehensive Introduction to Sub-Riemannian Geometry (2019, methodology): “In this chapter we develop a Sard-type result for a special class of Lipschitz functions that is taken from [Rif04].”