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[[alternative]]Minkowski dimensoin and quasiconformal mapping

By [[author]]江金城, [[author]]Jin-Ching Jiang, 江金城 and Jin-Ching Jiang

Abstract

[[abstract]]F.W.Gehring和J.Vasisala在他捫的論文"Hausdorff dimension and quasiconformal mapping"中,探討了一個集合的Hausdorff維度經過擬共 形變換後,會發生怎樣的變化。由於Minkowski維度在研究擬共形時,是 良好的幾何刻劃條件,因此本文就[G.V.]的結果為參考,探討 Minkowski 維度和擬共形變換的關係。我們證明了一個集合的Minkowski維度在0維 時,經擬共形變換後,像集的維度仍是0維。對任意介於0和n的兩個 數.alpha.和.beta.我們證明可找到擬共形及集合A和B其Minkowski維度 分別為.alpha.和.beta.,而擬共形將A映成B。並給出一個集合的 Minkowski維度在具有固定的K的擬共形變換下的像集維度的上下界。

Topics: Cantor集, Minkowski維度, 擬共形變換, Cantor set, Minkowski dimension, quasiconformal mapping, [[classification]]37
Year: 2010
OAI identifier: oai:ir.lib.ntnu.edu.tw:309250000Q/17622
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