5 papers · 1 filter
Uniformly branching trees
Mario Bonk, Daniel Meyer
A quasiconformal tree is a (compact) metric tree that is doubling and of bounded turning. We call trivalent if every branch point of has exactly three branches. If the…
Quotients of torus endomorphisms and Lattès-type maps
Mario Bonk, Daniel Meyer
We show that if an expanding Thurston map is the quotient of a torus endomorphism, then it has a parabolic orbifold and is a Lattès-type map.
Square Sierpiński carpets and Lattès maps
Mario Bonk, Sergei Merenkov
We prove that every quasisymmetric homeomorphism of a standard square Sierpiński carpet , odd, is an isometry. This strengthens and completes earlier work by the auth…
Uniformization by square domains
Mario Bonk
We find an extremal problem for conformal maps on a finitely connected subregion of the Riemann sphere containing the point at infinity whose unique solution is a map onto a square…
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 -…