1 citations · 1 across the 8 of their papers we have counts for
8 papers
Flatness, Menger curvature, and parametrization
Guy C. David, Vyron Vellis
We show that on linearly locally contractible (LLC) manifolds, the beta numbers (which describe unilateral flatness) are comparable to the theta numbers (which describe bilateral f…
The Heinonen-Semmes problems after thirty years
Guy C. David, Pekka Pankka, Jeremy T. Tyson
We survey the current status of the questions posed by Juha Heinonen and Stephen Semmes in `Thirty-three yes or no questions about mappings, measures, and metrics' (Conformal Geome…
An existence theorem for sliding minimal sets
Guy David, Camille Labourie
We prove an existence theorem for the sliding boundary variant of the Plateau problem for -dimensional sets in . The simplest case of sufficient condition is when…
Coarse and pointwise tangent fields
Guy C. David, Sylvester Eriksson-Bique, Raanan Schul
Alberti, Csörnyei and Preiss introduced a notion of a "pointwise (weak) tangent field" for a subset of Euclidean space -- a field that contains almost every tangent line of every c…
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…
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…
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…
Lower bounds on mapping content and quantitative factorization through trees
Guy C. David, Raanan Schul
We give a simple quantitative condition, involving the "mapping content" of Azzam--Schul, that implies that a Lipschitz map from a Euclidean space to a metric space must be close t…