10 citations · 43 across the 42 of their papers we have counts for
8 papers · 1 filter
Non-smooth sub-Riemannian manifolds with non-integer dimension and a Poincaré inequality
Sylvester Eriksson-Bique, Enrico Le Donne
For every integer and real number , we construct a -Ahlfors regular metric measure manifold of topological d…
Martingale and analytic dimensions
Sylvester Eriksson-Bique, Mathav Murugan
These notes introduce the martingale dimension of a strongly local regular Dirichlet form and the analytic dimension of a Lipschitz differentiability space. We explain why these di…
On universal elements for doubling geodesic trees
Sylvester Eriksson-Bique, Manisha Garg
For and , let denote the class of geodesic metric trees of valence at most whose branch points are uniformly relatively separated with c…
Embeddability and rectifiability of Lipschitz differentiability spaces
Ivan Caamano, Sylvester Eriksson-Bique, Elefterios Soultanis
We prove that Lipschitz differentiability spaces which bi-Lipschitz embed into an RNP-space are countably rectifiable. In contrast to earlier methods of Cheeger and Kleiner, our ap…
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 Sierpiński carpets do not attain their conformal dimension
Riku Anttila, Sylvester Eriksson-Bique
It is a long-standing open question to determine whether the Sierpiński carpet attains its conformal dimension or not. While this problem remains unresolved, we prove that Cartesia…
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 i…
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…