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math.CA2024
Factorization and piecewise affine approximation of bi-Lipschitz mappings on large sets
Guy C. David, Matthew Romney, Raanan Schul
A well-known open problem asks whether every bi-Lipschitz homeomorphism of factors as a composition of mappings of small distortion. We show that every bi-Lipschitz…
math.MG2024
Analytically one-dimensional planes and the Combinatorial Loewner Property
Guy C. David, Sylvester Eriksson-Bique
It is a major problem in analysis on metric spaces to understand when a metric space is quasisymmetric to a space with strong analytic structure, a so-called Loewner space. A conje…
math.CA2024
Quantitative metric density and connectivity for sets of positive measure
Guy C. David, Brandon Oliva
We show that in doubling, geodesic metric measure spaces (including, for example, Euclidean space), sets of positive measure have a certain large-scale metric density property. As…