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Showing 1 to 5 of 5 for “"Bi-Lipschitz"”.
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A characterization of Bi-Lipschitz embeddable metric spaces in terms of local Bi-Lipschitz embeddability
… complete, doubling metric spaces which embed bi-Lipschitzly into Euclidean space. Our result applies in particular to spaces of Grushin type equipped with Carnot-Carath ́eodory distance. Hence we obtain the first example of a sub-Riemannian manifold admitting such a bi-Lipschitz embedding. Our …
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Examples and Applications of Infinite Iterated Function Systems
… and sufficient conditions for such systems to be bi-Lipschitz equivalent. We use the concept of scaling functions to obtain some result about 1-dimensional systems. We discuss particular examples of infinite iterated function systems derived from complex continued fraction expansions with …
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Geometric mapping theory of the Heisenberg group, sub-Riemannian manifolds, and hyperbolic spaces
… every quasi-symmetry of $\Heis^n$ lifts to a bi-Lipschitz mapping of $\Hyp^{n+1}_\C$, providing a rigidity result for quasi-isometries of $\Hyp^{n+1}_\C$. We conclude by showing that if $\Gamma$ is a lattice in the isometry group of a non-compact rank one symmetric space (except $\Hyp^1_\C = …
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Geometry and analysis of Ricci curvature and mean curvature flows
… in the Gromov-Hausdorff sense. Together with Bing Wang we proved that the first (n+1)-eigenfunctions of Laplacian provides a bi-Holder diffeomorphism and we further give a counter-example showing that the bi-Holder estimate is sharp and cannot be improved to a bi-Lipschitz estimate. Thirdly, …
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Metric geometry of the Grushin plane and generalizations
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-03-13 without embargo terms