Poincaré不等式在Gromov-Hausdorff极限下的稳定性

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中图分类号：O174.5 文献标志码：A 文章编号：1673-3851（2025）11-0883-06引文格式：．Poincaré不等式在Gromov-Hausdorf极限下的稳定性[J]．浙江理工大学学报（自然科学），2025，53（6）：883-888.Reference Format：ZHU Tingjig，HAN Yecong，HUANG Tiren.Stabilityof Poincaré inequalityunder Gromov-Hausdorff limit[J]. Journal of Zhejiang Sci-Tech University，2025，53（6）：883-888.

Stability of Poincaré inequality under Gromov-Hausdorff limit

ZHU Tingjing，HAN Yecong，HUANG Tiren （School of Science，Zhejiang Sci-Tech University，Hangzhou 3lOol8，China）

Abstract： In this study，a suitable metric measure space was constructed by using the symmetric Riesz kernel representation method and the Radon-Nikodym theorem，and the stability of Poincaré inequality under the Gromov-Hausdorf limit was proved by using the convergence of the curve family module and the weak convergence of the doubling measure. We let a complete sequence of doubling metric measure spaces Gromov-Hausdorff converge to a complete metric measure space，and if the space sequence satisfies the Poincaré inequality， then the corresponding convergence space also satisfies the Poincaré inequality. This study enriches the stability of metric characteristics on metric spaces under Gromov-Hausdorff limit.

Key words： Poincaré inequality；Gromov-Hausdorff convergence； metric measure space；Riesz kernel; stability

0引言

近年来，Gromov-Hausdorff 极限是微分几何研究的热点问题。（剩余7268字）