Yamabe constant evolution and monotonicity along the conformal Ricci flow

Abstract

<abstract><p>We investigate the Yamabe constant's behaviour in a conformal Ricci flow. For conformal Ricci flow metric $ g(t) $, $ t \in [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) = g_0 $ is Yamabe metric, then the Yamabe constant is monotonically growing along the conformal Ricci flow under some simple assumptions unless $ g_0 $ is Einstein. As a result, this study adds to the body of knowledge about the Yamabe problem.</p></abstract>