论文标题
$ p $ - 绿色功能的单调性
Monotonicity of the $p$-Green functions
论文作者
论文摘要
在完整的$ p $ - 非副代理$ 3 $维歧管上，具有非负标量曲率和消失的第二个同源性，我们为$ 1 <p <3 $的级别设置了适当的$ p $ green函数的尖锐单调公式。在$ p = 2 $的情况下，这可以将其视为Munteanu-Wang \ cite {munteanuwang2021}对最新结果的概括。当$ 1 <p \ leq 2 $时，在$ p $ - 格林功能上没有平滑性假设。还证明了几个刚性结果。
On a complete $p$-nonparabolic $3$-dimensional manifold with non-negative scalar curvature and vanishing second homology, we establish a sharp monotonicity formula for the proper $p$-Green function along its level sets for $1<p<3$. This can be viewed as a generalization of the recent result by Munteanu-Wang \cite{MunteanuWang2021} in the case of $p=2$. No smoothness assumption is made on the $p$-Green function when $1<p\leq 2$. Several rigidity results are also proven.
