DC Calculus

Ambrosio Luigi - Bertrand Jerome

year: 2015
abstract: In this paper, we extend the DC Calculus introduced by Perelman on finite dimensional Alexandrov spaces with curvature bounded below. Among other things, our results allow us to define the Hessian and the Laplacian of DC functions (including distance functions as a particular instance) as a measure-valued tensor and a Radon measure respectively. We show that these objects share various properties with their analogues on smooth Riemannian manifolds.

The paper is available on the cvgmt preprint server.