Plane with A∞‐Weighted Metric not Bilipschitz Embeddable to Rn
Plane with A∞‐Weighted Metric not Bilipschitz Embeddable to Rn
复制标题
具有 A∞ 加权度量的平面，不可嵌入 Rn Bilipschitz
DOI：
10.1112/s0024609302001200
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发表时间：
2002
影响因子：
0.9
通讯作者：
T. Laakso
中科院分区：
文献类型：
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作者：
T. Laakso
构造了一个平面集G-⊂R2，它与(G，DZ)是bilipschitz等价的，其中(G，d)不是bilipschitz可嵌入到任何一致凸Banach空间的.这里，Z∈(0，1)和DZ表示度量d的Z次方.这证明了R2中存在强A Banach权，使得相应的变形几何不允许∞映射到任何一致凸的Banach空间.这样的权重不能与R2的拟共形自映射的雅可比比相媲美。2000年数学科目分类54E40(小学)；30C62、30C65、28A80(中学)。
A planar set G ⊂ R2 is constructed that is bilipschitz equivalent to (G,dz), where (G, d) is not bilipschitz embeddable to any uniformly convex Banach space. Here, Z ∈ (0, 1) and dz denotes the zth power of the metric d. This proves the existence of a strong A∞ weight in R2, such that the corresponding deformed geometry admits no bilipschitz mappings to any uniformly convex Banach space. Such a weight cannot be comparable to the Jacobian of a quasiconformal self‐mapping of R2. 2000 Mathematics Subject Classification 54E40 (primary); 30C62, 30C65, 28A80 (secondary).