| 度量空间中曲线族的模与共形维数 |
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| 引用本文： | 彭峰集.度量空间中曲线族的模与共形维数[J].湖北大学学报(自然科学版),2009,31(1):12-15. |
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| 作者姓名： | 彭峰集 |
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| 作者单位： | 湖北大学,数学与计算机科学学院,湖北,武汉,430062
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| 摘 要： | 设（X，μ）是紧的一致完全的加倍度量测度空间，p〉1．证明下面的结果：若（X，μ）有非凡p模且存在C〉0，使对任意球B有μ（B）≤C（r（B））^p，则X的共形维数至少为p，这里r（B）表示B的半径．
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| 关 键 词： | 曲线族的模 共形维数 拟对称映射 |
Modulus of curve families and conformal dimension in metric space |
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| PENG Feng-ji.Modulus of curve families and conformal dimension in metric space[J].Journal of Hubei University(Natural Science Edition),2009,31(1):12-15. |
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| Authors: | PENG Feng-ji |
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| Institution: | School of Mathematics and Computer Science;Hubei University;Wuhan 430062;China |
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| Abstract: | Suppose that （X,μ） is a compact and uniformly perfect doubling metric measure space and that p〉1. It obtains the following result. If X has nontrivial p-modulus and if there is a constant C〉0 such that μ（B）≤C（r（B））^p for any ball B belong to X, then the conformal dimension of X is at least p, where r（B） denotes the radius of B. |
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| Keywords: | modulus of a curve families conformal dimension quasisymmetric mapping |
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