论文标题
边界加权的山马问题
The weighted Yamabe problem with boundary
论文作者
论文摘要
我们介绍了Yamabe-type Flow \ begin {align*} \ left \ {\ begin {array} {ll} {ll} \ frac {\ partial g} {\ partial g} {\ partial t} ＆= \ frac {m} {2}（r^m_ϕ-r^m_ ϕ）\ end {array} \ right。 ~~ \ mbox {in} m ~~ \ mbox {and} ~~ h^m_ϕ = 0 ~~ \ mbox {on} \ partial m \ end m \ end eend {align*}在带有边界$ $ $ $ $ $ $的平稳度量上$ r^m_ϕ $是加权标量曲率的平均值，而$ h^m_ϕ $是加权平均曲率。我们证明了这种流程的长期存在和收敛性。
We introduce a Yamabe-type flow \begin{align*} \left\{ \begin{array}{ll} \frac{\partial g}{\partial t} &=(r^m_ϕ-R^m_ϕ)g \\ \frac{\partial ϕ}{\partial t} &=\frac{m}{2}(R^m_ϕ-r^m_ϕ) \end{array} \right. ~~\mbox{ in }M ~~\mbox{ and }~~ H^m_ϕ=0 ~~\mbox{ on }\partial M \end{align*} on a smooth metric measure space with boundary $(M,g, v^mdV_g,v^mdA_g,m)$, where $R^m_ϕ$ is the associated weighted scalar curvature, $r^m_ϕ$ is the average of the weighted scalar curvature, and $H^m_ϕ$ is the weighted mean curvature. We prove the long-time existence and convergence of this flow.
