Mathematische Zeitschrift

, Volume 288, Issue 3–4, pp 1037–1080 | Cite as

DC calculus

  • Luigi Ambrosio
  • Jérôme Bertrand


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.


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© Springer-Verlag GmbH Deutschland 2017

Authors and Affiliations

  1. 1.Scuola Normale SuperiorePisaItaly
  2. 2.Institut de Mathématiques de Toulouse, UMR CNRS 5219Université Toulouse IIIToulouse Cedex 9France

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