552 citations · 2k across the 45 of their papers we have counts for
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Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces
Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré
We compare several notion of weak (modulus of) gradient in metric measure spaces. Using tools from optimal transportation theory we prove density in energy of Lipschitz maps indepe…
Metric measure spaces with Riemannian Ricci curvature bounded from below
Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré
In this paper we introduce a synthetic notion of Riemannian Ricci bounds from below for metric measure spaces (X,d,m) which is stable under measured Gromov-Hausdorff convergence an…
Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré
This paper is devoted to a deeper understanding of the heat flow and to the refinement of calculus tools on metric measure spaces (X,d,m). Our main results are: - A general study o…