Rubens Longhi (UP)
We consider the volume-normalized Ricci flow close to compact shrinking Ricci solitons. We show that if a compact Ricci soliton (M,g) is a local maximum of Perelman's shrinker entropy, any normalized Ricci flow starting close to it exists for all time and converges towards a Ricci soliton. If g is not a local maximum of the shrinker entropy, we show that there exists a nontrivial normalized Ricci flow emerging from it. These theorems are analogues of results in the Ricci-flat and in the Einstein case.