Stability and instability of Ricci solitons

作者：Kroencke Klaus

来源：Calculus of Variations and Partial Differential Equations, 2015, 53(1-2): 265-287.

DOI：10.1007/s00526-014-0748-3

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 flowstarting 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 showthat 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 (Haslhofer and Muller, arXiv:1301.3219, 2013; Kroncke, arXiv: 1312.2224, 2013).

• 出版日期2015-5