$p$ -格林函数的单调性
Monotonicity of the $p$-Green functions
摘要：
在具有非负数量曲率和零次同调的完备$p$ -非抛物$p$-维流形上，我们建立了$1<p<3$的真$p$ -格林函数沿其水平集的尖锐单调性公式.这可以被看作是Munteanu-Wang \cite{MunteanuWang2021}在$p=2$情况下的最近结果的推广。当$p$.几个刚度的结果也被证明。
英文摘要：
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.
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