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• W2912234051 abstract "Let $W$ be a manifold with boundary $M$ given together with a conformal class $bar C$ which restricts to a conformal class $C$ on $M$. Then the relative Yamabe constant $Y_{bar C}(W,M;C)$ is well-defined. We study the short-time behavior of the relative Yamabe constant $Y_{[bar g_t]}(W,M;C)$ under the Ricci flow $bar g_t$ on $W$ with boundary conditions that mean curvature $H_{bar g_t}equiv 0$ and $bar{g}_t|_Min C = [bar{g}_0]$. In particular, we show that if the initial metric $bar{g}_0$ is a Yamabe metric, then, under some natural assumptions, $left.frac{d}{dt}right|_{t=0}Y_{[bar g_t]}(W,M;C)geq 0$ and is equal to zero if and only the metric $bar{g}_0$ is Einstein." @default.
• W2912234051 created "2019-02-21" @default.
• W2912234051 creator A5064797445 @default.
• W2912234051 creator A5085377595 @default.
• W2912234051 date "2019-01-31" @default.
• W2912234051 modified "2023-09-27" @default.
• W2912234051 title "Evolution of relative Yamabe constant under Ricci Flow" @default.
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