18 citations · 63 across the 25 of their papers we have counts for
4 papers · 1 filter
Hausdorff dimension of three-period orbits in Birkhoff billiards
Sergei Merenkov, Vadim Zharnitsky
We prove that the Hausdorff dimension of the set of three-period orbits in classical billiards is at most one. Moreover, if the set of three-period orbits has Hausdorff dimension o…
Quasisymmetric Koebe Uniformization
Sergei Merenkov, Kevin Wildrick
We study a quasisymmetric version of the classical Koebe uniformization theorem in the context of Ahlfors regular metric surfaces. In particular, we prove that an Ahlfors 2-regular…
Rigidity of Schottky sets
Mario Bonk, Bruce Kleiner, Sergei Merenkov
We call a complement of a union of at least three disjoint (round) open balls in the unit sphere S^n a Schottky set. We prove that every quasisymmetric homeomorphism of a Schottky…
Quasisymmetric rigidity of square Sierpinski carpets
Mario Bonk, Sergei Merenkov
We prove that every quasisymmetric self-homeomorphism of the standard 1/3-Sierpiński carpet is a Euclidean isometry. For carpets in a more general family, the standard -…