46 citations · 73 across the 7 of their papers we have counts for
16 papers
The quasi-periods of the Weierstrass zeta-function
Mario Bonk
We study the ratio of the pseudo-periods of the Weierstrass -function in dependence of the ratio of the generators of the underlying rank-2 lattice. We w…
Eliminating Thurston obstructions and controlling dynamics on curves
Mario Bonk, Mikhail Hlushchanka, Annina Iseli
Every Thurston map on a -sphere induces a pull-back operation on Jordan curves , where is the postcritical se…
Canonical embeddings of pairs of arcs
Mario Bonk, Alexandre Eremenko
We show that for given four points in the Riemann sphere and a given isotopy class of two disjoint arcs connecting these points in two pairs, there exists a unique configuration wi…
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.
Analysis on Metric Spaces
Mario Bonk, Luca Capogna, Piotr Hajłasz +2
This note is a survey of Analysis on Metric spaces, in connection with the upcoming AMS Mathematics Research Communities program in June 2020.
Quasiconformal and geodesic trees
Mario Bonk, Daniel Meyer
A quasiconformal tree is a metric tree that is doubling and of bounded turning. We prove that every quasiconformal tree is quasisymmetrically equivalent to a geodesic tree with Hau…
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…
Triebel-Lizorkin spaces on metric spaces via hyperbolic fillings
Mario Bonk, Eero Saksman, Tomás Soto
We give a new characterization of (homogeneous) Triebel-Lizorkin spaces in the smoothness range for a fairly general class of metric mea…
Sobolev spaces and hyperbolic fillings
Mario Bonk, Eero Saksman
Let be an Ahlfors -regular compact metric measure space, where . For we introduce a new (fractional) Sobolev space consisting of functions whose extensio…
Quasisymmetries of Sierpiński carpet Julia sets
Mario Bonk, Misha Lyubich, Sergei Merenkov
We prove that if is a quasisymmetric homeomorphism between Sierpiński carpets that are the Julia sets of postcritically-finite rational maps, then is the restriction of a M…
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 -…
Uniformization of Sierpiński carpets in the plane
Mario Bonk
Let , , be a countable collection of Jordan curves in the extended complex plane $\Sph$ that bound pairwise disjoint closed Jordan regions. If the Jordan curves are un…
Expanding Thurston Maps
Mario Bonk, Daniel Meyer
We study the dynamics of Thurston maps under iteration. These are branched covering maps of 2-spheres with a finite set of postcritical points. We also…
Covering properties of meromorphic functions, negative curvature and spherical geometry
Mario Bonk, Alexandre Eremenko
Every nonconstant meromorphic function in the plane univalently covers spherical discs of radii arbitrarily close to arctan(sqrt 8) ~ 70^\circ 32'. If in addition all critical poin…