2013/01/16 by Michael Bradford Williams, Williams, Michael Bradford
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG
paper · pdf · doi:10.48550/arxiv.1301.3945
23 pages; various improvements in exposition and organization
arxiv created 2015/06/19 · arxiv updated 2015/06/22
We consider four extended Ricci flow systems---that is, Ricci flow coupled with other geometric flows---and 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 Yang-Mills flow, and Ricci flow coupled with heat flow for the torsion of a metric-compatible 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.