On Bilipschitz Extensions in Real Banach Spaces
On Bilipschitz Extensions in Real Banach Spaces
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DOI：
10.1155/2013/765685
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发表时间：
2012-11
影响因子：
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通讯作者：
Manzi Huang;Yaxiang Li
中科院分区：
文献类型：
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作者：
Manzi Huang;Yaxiang Li
设和表示维数至少为2的真实的Banach空间，和是具有连通边界的有界域，是-QH同胚，是一致的。本文的主要目的是证明，推广到同胚，是bilipschitz当且仅当是bilipschitz在。在一个自然的附加条件下，维萨拉的一些公开问题的答案是肯定的。
Suppose that and denote real Banach spaces with dimension at least 2, that and are bounded domains with connected boundaries, that is an -QH homeomorphism, and that is uniform. The main aim of this paper is to prove that extends to a homeomorphism and is bilipschitz if and only if is bilipschitz in . The answer to some open problems of Vaisala is affirmative under a natural additional condition.