Abstract
As in topology, where one wants to understand the homeomorphism type of a given space, a basic question in the theory of quasisymmetric maps asks which metric spaces are quasisymmetrically homeomorphic. This question is extremely difficult in general. There are closed (compact without boundary) four-dimensional Riemannian manifolds that are homeomorphic but not quasisymmetrically homeomorphic [42]. An easier question asks which spaces can be embedded quasisymmetrically in a given space or in a space from a given collection. A beautiful and complete answer to this problem can be given in the case where the receiving space is Euclidean.
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© 2001 Springer Science+Business Media New York
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Heinonen, J. (2001). Quasisymmetric Embeddings of Metric Spaces in Euclidean Space. In: Lectures on Analysis on Metric Spaces. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0131-8_12
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DOI: https://doi.org/10.1007/978-1-4613-0131-8_12
Publisher Name: Springer, New York, NY
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