Zobrazeno 1 - 10
of 72
pro vyhledávání: '"Vellis Vyron"'
Autor:
Shaw, Eve, Vellis, Vyron
An important implication of Rademacher's Differentiation Theorem is that every Lipschitz curve $\Gamma$ infinitesimally looks like a line at almost all of its points in the sense that at $\mathcal{H}^1$-almost every point of $\Gamma$, the only weak t
Externí odkaz:
http://arxiv.org/abs/2409.13662
Autor:
Badger Matthew, Vellis Vyron
Publikováno v:
Analysis and Geometry in Metric Spaces, Vol 9, Iss 1, Pp 90-119 (2021)
We investigate the Hölder geometry of curves generated by iterated function systems (IFS) in a complete metric space. A theorem of Hata from 1985 asserts that every connected attractor of an IFS is locally connected and path-connected. We give a qua
Externí odkaz:
https://doaj.org/article/0c87905a11d6469086eb3426c0600bc0
We generalize a bi-Lipschitz extension result of David and Semmes from Euclidean spaces to complete metric measure spaces with controlled geometry (Ahlfors regularity and supporting a Poincar\'e inequality). In particular, we find sharp conditions on
Externí odkaz:
http://arxiv.org/abs/2307.06931
Autor:
Shaw, Eve, Vellis, Vyron
An infinite iterated function system (IIFS) is a countable collection of contraction maps on a compact metric space. In this paper we study the conditions under which the attractor of a such system admits a parameterization by a continuous or H\"olde
Externí odkaz:
http://arxiv.org/abs/2304.06012
Autor:
Vellis Vyron
Publikováno v:
Analysis and Geometry in Metric Spaces, Vol 4, Iss 1 (2016)
Let Ω be a planar Jordan domain and α > 0. We consider double-dome-like surfaces Σ(Ω, tα) over Ω where the height of the surface over any point x ∈ Ωequals dist(x, ∂Ω)α. We identify the necessary and sufficient conditions in terms of and
Externí odkaz:
https://doaj.org/article/eabab2647d5042a7b147a830ff21254e
The primary aim of this paper is to give topological obstructions to Cantor sets in $\mathbb{R}^3$ being Julia sets of uniformly quasiregular mappings. Our main tool is the genus of a Cantor set. We give a new construction of a genus $g$ Cantor set,
Externí odkaz:
http://arxiv.org/abs/2210.06619
Autor:
Ramirez, Anthony, Vellis, Vyron
The Analyst's Traveling Salesman Problem asks for conditions under which a (finite or infinite) subset of $\mathbb{R}^N$ is contained on a curve of finite length. We show that for finite sets, the algorithm constructed by Schul (2007)and Badger-Naple
Externí odkaz:
http://arxiv.org/abs/2202.10314
A quasiconformal tree is a doubling metric tree in which the diameter of each arc is bounded above by a fixed multiple of the distance between its endpoints. In this paper we show that every quasiconformal tree bi-Lipschitz embeds in some Euclidean s
Externí odkaz:
http://arxiv.org/abs/2106.13007
Autor:
Fletcher, Alastair N., Vellis, Vyron
The Decomposition Problem in the class $LIP(\mathbb{S}^2)$ is to decompose any bi-Lipschitz map $f:\mathbb{S}^2 \to \mathbb{S}^2$ as a composition of finitely many maps of arbitrarily small isometric distortion. In this paper, we construct a decompos
Externí odkaz:
http://arxiv.org/abs/2106.00054
Autor:
David, Guy C., Vellis, Vyron
A quasiconformal tree is a doubling metric tree in which the diameter of each arc is bounded above by a fixed multiple of the distance between its endpoints. We study the geometry of these trees in two directions. First, we construct a catalog of met
Externí odkaz:
http://arxiv.org/abs/2007.12297