Bilipschitz Embeddings of Metric Spaces into Space Forms

By U. Lang, C. Plaut. 2001

140 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d10c141d391d3dafdc1a145371e706ca0c5219c7

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Products of Lipschitz-free spaces and applications (2014, methodology): “I thank Florent Baudier for driving my attention to [11].”
Assouad Dimension and Fractal Geometry (2020, unknown): “Another wellknown example of a doubling space which cannot embed into Euclidean space via a bi-Lipschitz mapping is a construction of Lang and Plaut [178] based on Laakso graphs, see [177].”
Nagata dimension, quasisymmetric embeddings, and Lipschitz extensions (2004, unknown): “Finally, in section 5, we resume our investigation [14], [15], [16], [17] of the extendability of Lipschitz maps.”
Markov chains in smooth Banach spaces and Gromov hyperbolic metric spaces (2004, background): “The standard example showing that in both embedding results we must pass to a power of the metric is the family of graphs known as the Laakso graphs [37, 38], which are planar graphs whose graph metric is uniformly doubling, yet they do not uniformly embed into Hilbert space.”
Bridgeland-stable moduli spaces for $K$-trivial surfaces (2007, background): “gt; X t∈Tk E h d(Xt,Xet(t−2k))p i 2kp >|Tk|· 2−(2m+3)p−1 &4h−2 ·4m−h−1 ·2−(2m+3)p−1 & 1 8p 4−m(p−1). (31) A combination of (30) and (31) implies (29). Proof of Theorem 1.5. As explained in [12, 13], by passing to an appropriate Gromov-Hausdorﬀ limit, there exists a doubling metric space (”
Assouad's theorem with dimension independent of the snowflaking (2010, methodology): “For a discussion of this important question, see for example the works of Semmes [28], Lang-Plaut [20] and Heinonen [16].”
Geometric embeddings of metric spaces (2003, unknown): “Read more in [61], [62], [65], [48], [45], [46].”