Abstract
We consider dynamical stability for a modified Ricci flow equation whose stationary solutions include Einstein and Ricci soliton metrics. Our focus is on homogeneous metrics on non-compact manifolds. Following the program of Guenther, Isenberg, and Knopf, we define a class of weighted little Hölder spaces with certain interpolation properties that allow the use of maximal regularity theory and the application of a stability theorem of Simonett. With this, we derive two stability theorems, one for a class of Einstein metrics and one for a class of non-Einstein Ricci solitons. Using linear stability results of Jablonski, Petersen, and the first author, we obtain dynamical stability for many specific Einstein and Ricci soliton metrics on simply connected solvable Lie groups.
Funding source: AMS-Simons
Award Identifier / Grant number: travel grant
Funding source: National Science Foundation
Award Identifier / Grant number: 0932078 000
Both authors thank Dan Knopf for helpful conversations and appreciate the hospitality of the Park City Mathematics Institute where part of this research was conducted.
© 2016 by De Gruyter
