球面化下保持均匀性、倍增测度与庞加莱不等式的锐利条件
Sharp conditions for preserving uniformity, doubling measure and Poincaré inequality under sphericalization
AI总结：
本文研究球面化变换，给出变形密度函数保持空间均匀性、测度倍增性质和庞加莱不等式支撑的锐利条件，并用例子证明条件的不可改进性。
摘要：
我们研究球面化，这是一种对无界度量测度空间的度量与测度进行共形变形，从而使变形后的空间有界的映射。本文的目标是研究变形密度函数上的锐利条件，在这些条件下，球面化保持空间的均匀性、测度的倍增性质以及庞加莱不等式的支撑。我们还提供了展示这些条件锐利性的例子。
英文摘要：
We study sphericalization, which is a mapping that conformally deforms the metric and the measure of an unbounded metric measure space so that the deformed space is bounded. The goal of this paper is to study sharp conditions on the deforming density function under which the sphericalization preserves uniformity of the space, the doubling property of the measure and the support of a Poincaré inequality. We also provide examples that demonstrate the sharpness of our conditions.
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。
