214 citations · 485 across the 38 of their papers we have counts for
4 papers · 1 filter
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…
Perelman's Entropy Functional at Type I Singularities of the Ricci Flow
Carlo Mantegazza, Reto Müller
We study blow-ups around fixed points at Type I singularities of the Ricci flow on closed manifolds using Perelman's W-functional. First, we give an alternative proof of the result…
A note on Codazzi tensors
Giovanni Catino, Carlo Mantegazza, Lorenzo Mazzieri
We discuss a gap in Besse's book, recently pointed out by Merton, which concerns the classification of Riemannian manifolds admitting a Codazzi tensors with exactly two distinct ei…
The Cotton tensor and the Ricci flow
Carlo Mantegazza, Samuele Mongodi, Michele Rimoldi
We compute the evolution equation of the Cotton and the Bach tensor under the Ricci flow of a Riemannian manifold, with particular attention to the three dimensional case, and we d…