度量测度空间的数量性质A、Poincare不等式、L^p-压缩和L^p-畸变
Quantitative property A, Poincare inequalities, L^p-compression and L^p-distortion for metric measure spaces
摘要：
为了估计度量测度空间X的L^p-压缩，我们引入了性质A的一个定量形式。我们得到各种估计的空间次指数体积增长。这个数量性质A也可以用来给出有限度量空间的L^p-畸变的上界。也就是说，我们得到了关于齐次黎曼流形的有限子集的新的最优结果。我们还介绍了一个一般形式的庞加莱不等式，提供压缩的限制，和失真的下界。这些不等式被用来证明我们的一些结果的最优性。
英文摘要：
We introduce a quantitative version of Property A in order to estimate the L^p-compressions of a metric measure space X. We obtain various estimates for spaces with sub-exponential volume growth. This quantitative property A also appears to be useful to yield upper bounds on the L^p-distortion of finite metric spaces. Namely, we obtain new optimal results for finite subsets of homogeneous Riemannian manifolds. We also introduce a general form of Poincare inequalities that provide constraints on compressions, and lower bounds on distortion. These inequalities are used to prove the optimality of some of our results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
