论文标题
统一的庞加莱不平等现象的公制空间
Uniform Poincaré inequalities on measured metric spaces
论文作者
论文摘要
考虑一个适当的地理公制空间$（x，d）$，配备了borel量$μ。$。如果满足当地的庞加莱不平等（$ p _ {loc} $），则在$（x，d，μ）上建立一个统一的庞加莱不平等家庭，并且体积的增长条件。因此，如果$μ$加倍并支持$（p_ {loc}）$，则它满足$（σ，β，σ）$ - poincaré不平等。如果$（x，d，μ）$是$δ$ - 文论空间，则使用\ cite {bcs}中的体积比较定理，我们获得了统一的庞加莱不平等，并具有庞加莱常数的指数增长。如果$ x $是紧凑型$ cd（k，\ infty）$空间的通用封面，那么它支持统一的庞加莱不平等，而庞加莱的常数取决于基本组的增长。
Consider a proper geodesic metric space $(X,d)$ equipped with a Borel measure $μ.$ We establish a family of uniform Poincaré inequalities on $(X,d,μ)$ if it satisfies a local Poincaré inequality ($P_{loc}$) and a condition on growth of volume. Consequently if $μ$ is doubling and supports $(P_{loc})$ then it satisfies a $(σ,β,σ)$-Poincaré inequality. If $(X,d,μ)$ is a $δ$-hyperbolic space then using the volume comparison theorem in \cite{BCS} we obtain a uniform Poincaré inequality with exponential growth of the Poincaré constant. If $X$ is the universal cover of a compact $CD(K,\infty)$ space then it supports a uniform Poincaré inequality and the Poincaré constant depends on the growth of the fundamental group.
