Zobrazeno 1 - 10
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pro vyhledávání: '"Wildrick Kevin"'
Autor:
Wildrick, Kevin
Among all Poincar\'e 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 $\iota$ of any Cheeger fractal $X$ into any Banach space $V$ with the
Externí odkaz:
http://arxiv.org/abs/2307.10857
Publikováno v:
Analysis and Geometry in Metric Spaces, Vol 1, Iss 2013, Pp 232-254 (2013)
We quantify the extent to which a supercritical Sobolev mapping can increase the dimension of subsets of its domain, in the setting of metric measure spaces supporting a Poincaré inequality. We show that the set of mappings that distort the dimensio
Externí odkaz:
https://doaj.org/article/a95c7163865e4b118a80546e491b7a42
Autor:
Geyer, Lukas, Wildrick, Kevin
Publikováno v:
Proc. Amer. Math. Soc. 146 (2018), no. 1, 281-293
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 quantitative way. We extend this result to arbitrary metric compact orientable s
Externí odkaz:
http://arxiv.org/abs/1610.08896
We construct a quasiconformal mapping of $n$-dimensional Euclidean space, $n \geq 2$, that simultaneously distorts the Hausdorff dimension of a nearly maximal collection of parallel lines by a given amount. This answers a question of Balogh, Monti, a
Externí odkaz:
http://arxiv.org/abs/1601.07205
Autor:
Iseli, Annina, Wildrick, Kevin
Publikováno v:
Conformal Geometry and Dynamics, Volume 21, pages 78-100, 2016
We consider a class of iterated function systems (IFSs) of contracting similarities of $R^n$, introduced by Hutchinson, for which the invariant set possesses a natural H\"older continuous parameterization by the unit interval. When such an invariant
Externí odkaz:
http://arxiv.org/abs/1512.04688
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 imply that the mapping in question satisfies some weak form of the co
Externí odkaz:
http://arxiv.org/abs/1308.5074
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 estimate, in terms of Euclidean Hausdorff dimension, the size of the set of
Externí odkaz:
http://arxiv.org/abs/1303.7094
Autor:
Wildrick, Kevin, Zürcher, Thomas
We give a sharp condition on the lower local Lipschitz constant of a mapping from a metric space supporting a Poincar\'e inequality to a Banach space with the Radon-Nikodym property that guarantees differentiability at almost every point. We apply th
Externí odkaz:
http://arxiv.org/abs/1208.2133
Publikováno v:
Geom. Funct. Anal. Volume 23, Number 3 (2013), 985-1034
A carpet is a metric space homeomorphic to the Sierpinski carpet. We characterize, within a certain class of examples, non-self-similar carpets supporting curve families of nontrivial modulus and supporting Poincar\'e inequalities. Our results yield
Externí odkaz:
http://arxiv.org/abs/1201.3548
Autor:
Merenkov, Sergei, Wildrick, Kevin
We study a quasisymmetric version of the classical Koebe uniformization theorem in the context of Ahlfors regular metric surfaces. In particular, we prove that an Ahlfors 2-regular metric surface X homeomorphic to a finitely connected domain in the s
Externí odkaz:
http://arxiv.org/abs/1109.3441