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Lectures on Analysis on Metric Spaces
TLDR
Theoretically, doubling measures and quasisymmetric maps have been studied in the context of Euclidean spaces in this article, where doubling measures have been shown to be equivalent to Poincare inequalities.Abstract:
1. Covering Theorems.- 2. Maximal Functions.- 3. Sobolev Spaces.- 4. Poincare Inequality.- 5. Sobolev Spaces on Metric Spaces.- 6. Lipschitz Functions.- 7. Modulus of a Curve Family, Capacity, and Upper Gradients.- 8. Loewner Spaces.- 9. Loewner Spaces and Poincare Inequalities.- 10. Quasisymmetric Maps: Basic Theory I.- 11. Quasisymmetric Maps: Basic Theory II.- 12. Quasisymmetric Embeddings of Metric Spaces in Euclidean Space.- 13. Existence of Doubling Measures.- 14. Doubling Measures and Quasisymmetric Maps.- 15. Conformal Gauges.- References.read more
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Optimal Transport: Old and New
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Journal ArticleDOI
On the geometry of metric measure spaces. II
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Sobolev met Poincaré
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Locality-sensitive binary codes from shift-invariant kernels
Maxim Raginsky,Svetlana Lazebnik +1 more
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Proceedings ArticleDOI
Bounded geometries, fractals, and low-distortion embeddings
TL;DR: This work considers both general doubling metrics, as well as more restricted families such as those arising from trees, from graphs excluding a fixed minor, and from snowflaked metrics, which contains many families of metrics that occur in applied settings.