Yamabe constant evolution and monotonicity along the conformal Ricci flow

Abstract

We investigate the Yamabe constant's behaviour in a conformal Ricci flow. For conformal Ricci flow metric g(t), t∈[0,T), the time evolution formula for the Yamabe constant Y(g(t)) is derived. It is demonstrated that if the beginning metric g(0)=g0 is Yamabe metric, then the Yamabe constant is monotonically growing along the conformal Ricci flow under some simple assumptions unless g0 is Einstein. As a result, this study adds to the body of knowledge about the Yamabe problem.

Keywords

• yamabe constant
• conformal ricci flow
• einstein metric
• scalar curvature