14 papers
Quantitative non-embeddability theorems and metric embeddings of slit carpets
Sylvester Eriksson-Bique, Niilo Joutsenlahti
We study the bi-Lipschitz embedding problem for a class of metric spaces called slit carpets. First we show that the th stage of the standard slit carpet of Meren…
Cartesian products of SierpiÅski carpets do not attain their conformal dimension
Riku Anttila, Sylvester Eriksson-Bique
It is a long-standing open question to determine whether the SierpiÅski carpet attains its conformal dimension or not. While this problem remains unresolved, we prove that Cartesi…
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…
On the Resistance Conjecture
Sylvester Eriksson-Bique
We give an affirmative answer to the resistance conjecture on characterization of parabolic Harnack inequalities in terms of volume doubling, upper capacity bounds and a Poincaré…
Traces of Newton-Sobolev functions on the visible boundary of domains in doubling metric measure spaces supporting a -Poincaré inequality
Sylvester Eriksson-Bique, Ryan Gibara, Riikka Korte +1
We consider the question of whether a domain with uniformly thick boundary at all locations and at all scales has a large portion of its boundary visible from the interior; here, "…
Conformal dimension and its attainment on self-similar Laakso-type fractal spaces
Riku Anttila, Sylvester Eriksson-Bique, Lassi Rainio
A general construction of Laakso-type fractal spaces was recently introduced by the first two authors. In this paper, we establish a simple condition characterizing when the Ahlfor…