40 citations · 79 across the 9 of their papers we have counts for
13 papers
Bochner Partial Derivatives, Cheeger-Kleiner Differentiability, and Non-Embedding
Kevin Wildrick
Among all Poincaré inequality spaces, we define the class of Cheeger fractals, which includes the sub-Riemannian Heisenberg group. We show that there is no bi-Lipschitz embedding $…
Quantitative quasisymmetric uniformization of compact surfaces
Lukas Geyer, Kevin Wildrick
Bonk and Kleiner showed that any metric sphere which is Ahlfors 2-regular and linearly locally contractible is quasisymmetrically equivalent to the standard sphere, in a quantitati…
Quasiconformal mappings that highly distort dimensions of many parallel lines
Zoltán M. Balogh, Jeremy T. Tyson, Kevin Wildrick
We construct a quasiconformal mapping of -dimensional Euclidean space, , that simultaneously distorts the Hausdorff dimension of a nearly maximal collection of paralle…
Iterated function system quasiarcs
Annina Iseli, Kevin Wildrick
We consider a class of iterated function systems (IFSs) of contracting similarities of , introduced by Hutchinson, for which the invariant set possesses a natural Hölder conti…
Weak contact equations for mappings into Heisenberg groups
Zoltán M. Balogh, Piotr Hajłasz, Kevin Wildrick
Let k>n be positive integers. We consider mappings from a subset of k-dimensional Euclidean space R^k to the Heisenberg group H^n with a variety of metric properties, each of which…
Frequency of Sobolev dimension distortion of horizontal subgroups of Heisenberg groups
Zoltán M. Balogh, Jeremy T. Tyson, Kevin Wildrick
We study the behavior of Sobolev mappings defined on the Heisenberg groups with respect to a foliation by left cosets of a horizontal homogeneous subgroup. We quantitatively estima…