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Yamabe constant evolution and monotonicity along the conformal Ricci flow
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<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>
American Institute of Mathematical Sciences (AIMS)
Title: Yamabe constant evolution and monotonicity along the conformal Ricci flow
Description:
<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>.
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