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math.FA2012★ 260 cited
Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds
Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré
The aim of the present paper is to bridge the gap between the Bakry-Émery and the Lott-Sturm-Villani approaches to provide synthetic and abstract notions of lower Ricci curvature b…
math.FA2012★ 1 cited
A Flow Tangent to the Ricci Flow via Heat Kernels and Mass Transport
Nicola Gigli, Carlo Mantegazza
We present a new relation between the short time behavior of the heat flow, the geometry of optimal transport and the Ricci flow. We also show how this relation can be used to defi…