3 citations · 3 across the 10 of their papers we have counts for
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Projection theorems for linear-fractional families of projections
Anton Lukyanenko, Annina Iseli
Marstrand's theorem states that applying a generic rotation to a planar set before projecting it orthogonally to the -axis almost surely gives an image with the maximal poss…
Quasiconvexity in the Heisenberg group
David A. Herron, Anton Lukyanenko, Jeremy T. Tyson
We show that if is a closed subset of the Heisenberg group whose vertical projections are nowhere dense, then the complement of is quasiconvex. In particular, closed sets w…
Separated Nets in Nilpotent Groups
Tullia Dymarz, Michael Kelly, Sean Li +1
In this paper we generalize several results on separated nets in Euclidean space to separated nets in connected simply connected nilpotent Lie groups. We show that every such group…
Quasiregular mappings on sub-Riemannian manifolds
Katrin Fassler, Anton Lukyanenko, Kirsi Peltonen
We study mappings on sub-Riemannian manifolds which are quasi-regular with respect to the Carnot-Caratheodory distances and discuss several related notions. On H-type Carnot groups…