7 citations · 13 across the 6 of their papers we have counts for
9 papers
Grand orbit relations in wandering domains
Vasiliki Evdoridou, Núria Fagella, Lukas Geyer +1
One of the fundamental distinctions in McMullen and Sullivan's description of the Teichmüller space of a complex dynamical system is between discrete and indiscrete grand orbit rel…
Classification of critically fixed anti-Thurston maps
Lukas Geyer, Mikhail Hlushchanka
We provide a complete combinatorial classification of critically fixed anti-Thurston maps, i.e., orientation-reversing branched covers of the 2-sphere that fix every critical point…
Expanding metrics for unicritical semihyperbolic polynomials
Lukas Geyer
We prove that unicritical polynomials which are semihyperbolic, i.e., for which the critical point is a non-recurrent point in the Julia set, are uniformly expandi…
Quantitative quasisymmetric uniformization of compact surfaces
Lukas Geyer, Kevin Wildrick
Bonk and Kleiner showed that any metric sphere which is Ahlfors 2-regular and linearly locally contractible is quasisymmetrically equivalent to the standard sphere, in a quantitati…
Linearizability of Saturated Polynomials
Lukas Geyer
Brjuno and Rüssmann proved that every irrationally indifferent fixed point of an analytic function with a Brjuno rotation number is linearizable, and Yoccoz proved that this is sha…
On the exceptional set in a conditional theorem of Littlewood
Lukas Geyer
In 1952, Littlewood stated a conjecture about the average growth of spherical derivatives of polynomials, and showed that it would imply that for entire function of finite order, "…
Smooth Siegel disks without number theory: A remark on a proof by Buff and Cheritat
Lukas Geyer
X. Buff and A. Cheritat proved that there are quadratic polynomials having Siegel disks with smooth boundaries. Based on a simplification of A. Avila, we give yet another simplific…
Sharp bounds for the valence of certain harmonic polynomials
Lukas Geyer
D. Khavinson and G. Swiatek proved that harmonic polynomials p(z)+q(z), where p is holomorphic, q is antiholomorphic, and deg p = n > 1 = deg q, can have at most 3n-2 complex zeros…
A Hyperbolic Surface With A Square Grid Net
Lukas Geyer, Sergei Merenkov
We prove the existence of a hyperbolic surface spread over the sphere for which the projection map has all its singular values on the extended real line, and such that the preimage…