Journal of the
Korean Mathematical Society JKMS

In this paper, we introduce a general Ricci flow system, which is closely linked with the Ricci flow and the renormalization group flow, etc. We prove the short-time existence, the entropy functionals, the higher derivatives estimates and the compactness theorem for this general Ricci flow system on closed Riemannian manifolds. These basic results are useful tools to understand the singularities of this system.

Keywords: Ricci flow, renormalization group flow, B-field, static Einstein vacuum equations, entropy, gradient estimates, compactness theorem

MSC numbers: Primary 53C44; Secondary 35K55, 35P15