论文标题
亚谐波功能，保形度量和CAT（0）
Subharmonic Functions, Conformal Metrics, and CAT(0)
论文作者
论文摘要
我们提供了一个分析证明，表明某些天然公平均覆盖物是Hadamard度量空间。特别是，如果$ρ=φ\ circ u $，其中$ u $是本地Lipschitz和$ω$的subharmonic，$φ$是积极的，并且在包含$ u（ω）$的间隔中增加，$ \logφ$ convex，并且如果衡量标准$（ω，ρ（ρ（Z）| dz | DZ | DZ | DZ | DZ | DZ） $（\tildeΩ，\ tilde {d}）$，这是哈达玛的空间，地球仪具有Lipschitz连续的第一衍生物。
We present an analytical proof that certain natural metric planar universal covers are Hadamard metric spaces. In particular if $ρ=φ\circ u$ where $u$ is locally Lipschitz and subharmonic in $Ω$, $φ$ is positive and increasing on an interval containing $u(Ω)$ with $\logφ$ convex, and if the metric space $(Ω,ρ(z)|dz|)$ is complete, then it has universal cover $(\tildeΩ,\tilde{d})$ which is a Hadamard space for which geodesics have Lipschitz continuous first derivatives.
