Stability of solutions of certain extended Ricci flow systems
Michael Bradford Williams,
2013.01.16
http://arxiv.org/abs/1301.3945
We consider four extended Ricci flow systemsthat is, Ricci flow coupled
with other geometric flowsand prove dynamical stability of certain classes
of stationary solutions of these flows. The systems include Ricci flow coupled
with harmonic map flow (studied abstractly and in the context of Ricci flow on
warped products), Ricci flow coupled with both harmonic map flow and YangMills
flow, and Ricci flow coupled with heat flow for the torsion of a
metriccompatible connection. The methods used to prove stability follow a
program outlined by Guenther, Isenberg, and Knopf, which uses maximal
regularity theory for quasilinear parabolic systems and a result of Simonett.
