DC Calculus
Differential Geometry
2015-05-20 v1 Metric Geometry
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.
Cite
@article{arxiv.1505.04817,
title = {DC Calculus},
author = {Luigi Ambrosio and Jérôme Bertrand},
journal= {arXiv preprint arXiv:1505.04817},
year = {2015}
}