10 citations · 34 across the 13 of their papers we have counts for
14 papers
Quasisymmetric universality, quasi-isometric classification and topological rigidity of Kleinian groups
Peter Haïssinsky, Yusheng Luo
We study the quasisymmetric classification of limit sets of Kleinian groups and obtain a characterization of those geometrically finite limit sets that are quasisymmetrically unive…
Circle packings, renormalizations and subdivision rules
Yusheng Luo, Yongquan Zhang
In this paper, we use iterations of skinning maps on Teichmüller spaces to study circle packings and develop a renormalization theory for circle packings whose nerves satisfy certa…
Polynomials with core entropy zero
Yusheng Luo, Insung Park
This paper studies polynomials with core entropy zero. We give several characterizations of polynomials with core entropy zero. In particular, we show that a degree d post-critical…
On Deformation Space Analogies between Kleinian Reflection Groups and Antiholomorphic Rational Maps
Russell Lodge, Yusheng Luo, Sabyasachi Mukherjee
In a previous paper, we constructed an explicit dynamical correspondence between certain Kleinian reflection groups and certain anti-holomorphic rational maps on the Riemann sphere…
On geometrically finite degenerations II: convergence and divergence
Yusheng Luo
In this paper, we study quasi post-critically finite degenerations for rational maps. We construct limits for such degenerations as geometrically finite rational maps on a finite t…
On geometrically finite degenerations I: boundaries of main hyperbolic components
Yusheng Luo
In this paper, we develop a theory on the degenerations of Blaschke products to study the boundaries of hyperbolic components. We give a combinatorial classificatio…
Circle packings, kissing reflection groups and critically fixed anti-rational maps
Russell Lodge, Yusheng Luo, Sabyasachi Mukherjee
In this paper, we establish an explicit correspondence between kissing reflection groups and critically fixed anti-rational maps. The correspondence, which is expressed using simpl…
On hyperbolic rational maps with finitely connected Fatou sets
Yusheng Luo
In this paper, we study hyperbolic rational maps with finitely connected Fatou sets. We construct models of post-critically finite hyperbolic tree mapping schemes for such maps, ge…
Trees, length spectra for rational maps via barycentric extensions and Berkovich spaces
Yusheng Luo
In this paper, we study the dynamics of degenerating sequences of rational maps on Riemann sphere using -trees. Given a sequence of degenerating rati…
Limits of rational maps, R-trees and barycentric extension
Yusheng Luo
In this paper, we show that one can naturally associate a limiting dynamical system on an -tree to any degenerating sequence of rational maps $f_n: \hat…
On the inhomogeneity of the Mandelbrot set
Yusheng Luo
We will show the Mandelbrot set is locally conformally inhomogeneous: the only conformal map defined in an open set intersecting and satisfying $f(U\cap\pa…
Moser's Shadow Problem
Jeffrey C. Lagarias, Yusheng Luo, Arnau Padrol
Moser's shadow problem asks to estimate the shadow function , which is the largest number such that for each bounded convex polyhedron with vertices in $…
Weakly Circle-Preserving Maps in Inversive Geometry
Joel C. Gibbons, Yusheng Luo
Let S^n be the standard n-sphere embedded in R^{n+1}. A mapping T: S^n \to S^n, not assumed continuous or even measurable, nor injective, is called weakly circle-preserving if the…
Colorings of the n-sphere and inversive geometry
Joel C. Gibbons, Yusheng Luo
This paper shows that in dimensions n \geq 2 for any partition of the set of points in the standard n-sphere \sum_{i=0}^n x_i^2 =1 in R^{n+1} into (n+3) or more nonempty sets, ther…