10 citations · 43 across the 42 of their papers we have counts for
5 papers · 1 filter
Nilpotent groups and biLipschitz embeddings into
Sylvester Eriksson-Bique, Chris Gartland, Enrico Le Donne +2
We prove that if a simply connected nilpotent Lie group quasi-isometrically embeds into an space, then it is abelian. We reach this conclusion by proving that every Carnot gr…
Isoperimetric and Poincaré inequalities on non-self-similar Sierpiński sponges: the borderline case
Sylvester Eriksson-Bique, Jasun Gong
In this paper we construct a large family of examples of subsets of Euclidean space that support a 1-Poincaré inequality yet have empty interior. These examples are formed from an…
Bi-Lipschitz embeddings of quasiconformal trees
Guy C. David, Sylvester Eriksson-Bique, Vyron Vellis
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…
Curvewise characterizations of minimal upper gradients and the construction of a Sobolev differential
Sylvester Eriksson-Bique, Elefterios Soultanis
We represent minimal upper gradients of Newtonian functions, in the range , by maximal directional derivatives along "generic" curves passing through a given point,…
On the Sharp Lower Bound for Duality of Modulus
Sylvester Eriksson-Bique, Pietro Poggi-Corradini
We establish a sharp reciprocity inequality for modulus in compact metric spaces with finite Hausdorff measure. In particular, when is also homeomorphic to a planar rectang…