# Stability and instability of Ricci solitons

#### Autoren: Klaus Kröncke (2015)

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.

Zeitschrift:
Calc. Var. Partial Differ. Equ.
Verlag:
Springer
Seiten:
265-287
Band:
53, no.1-2

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