10 citations · 43 across the 42 of their papers we have counts for
4 papers · 1 filter
Pointwise inequalities for Sobolev functions on outward cuspidal domains
Sylvester Eriksson-Bique, Pekka Koskela, Jan Maly +1
We show that the first order Sobolev spaces on cuspidal symmetric domains can be characterized via pointwise inequalities. In particular, they coincide with the Hajlasz-Sobolev spa…
Thin Loewner carpets and their quasisymmetric embeddings in
Jeff Cheeger, Sylvester Eriksson-Bique
A carpet is a metric space which is homeomorphic to the standard Sierpiński carpet in , or equivalently, in . A carpet is called thin if its Hausdorff dimension…
Almost uniform domains and Poincaré inequalities
Sylvester Eriksson-Bique, Jasun Gong
Here we show existence of numerous subsets of Euclidean and metric spaces that, despite having empty interior, still support Poincaré inequalities. Most importantly, our methods do…
Regular mappings and non-existence of bi-Lipschitz embeddings for slit carpets
Guy C. David, Sylvester Eriksson-Bique
We prove that the "slit carpet" introduced by Merenkov does not admit a bi-Lipschitz embedding into any uniformly convex Banach space. In particular, this includes any Euclidean sp…