19 citations · 122 across the 20 of their papers we have counts for
23 papers
Uniformization of Julia sets of geometrically finite rational maps
Yusheng Luo, Dimitrios Ntalampekos
A Schottky set is the complement of a collection of disjoint open disks in the Riemann sphere. We completely characterize geometrically finite rational maps whose Julia sets are qu…
Conformal rigidity: progress and challenges
Dimitrios Ntalampekos, Malik Younsi
A domain in the Riemann sphere is called a \textit{circle domain} if every connected component of its boundary is either a round circle or a single point. A circle domain is \texti…
Koebe uniformization, John domains, and transboundary modulus
Christina Karafyllia, Dimitrios Ntalampekos
We prove Koebe's conjecture for John domains by showing that every planar John domain is conformally equivalent to a circle domain. Our proof is based on a geometric property of Jo…
Uniformization of Gromov hyperbolic domains by circle domains
Christina Karafyllia, Dimitrios Ntalampekos
We prove that a domain in the Riemann sphere is Gromov hyperbolic if and only if it is conformally equivalent to a uniform circle domain. This resolves a conjecture of Bonk--Heinon…
Exhaustions of circle domains
Dimitrios Ntalampekos, Kai Rajala
Koebe's conjecture asserts that every domain in the Riemann sphere is conformally equivalent to a circle domain. We prove that every domain satisfying Koebe's conjecture admits…
Lipschitz-Volume rigidity and Sobolev coarea inequality for metric surfaces
Damaris Meier, Dimitrios Ntalampekos
We prove that every 1-Lipschitz map from a closed metric surface onto a closed Riemannian surface that has the same area is an isometry. If we replace the target space with a non-s…
CNED sets: countably negligible for extremal distances
Dimitrios Ntalampekos
The author has recently introduced the class of CNED sets in Euclidean space, generalizing the classical notion of NED sets, and shown that they are quasiconformally removable. A s…
Rigidity and continuous extension for conformal maps of circle domains
Dimitrios Ntalampekos
We present sufficient conditions so that a conformal map between planar domains whose boundary components are Jordan curves or points has a continuous or homeomorphic extension to…
Conformal uniformization of planar packings by disk packings
Dimitrios Ntalampekos
A Sierpiński packing in the -sphere is a countable collection of disjoint, non-separating continua with diameters shrinking to zero. We show that any Sierpiński packing by conti…
Polyhedral approximation and uniformization for non-length surfaces
Dimitrios Ntalampekos, Matthew Romney
We prove that any metric surface (that is, metric space homeomorphic to a 2-manifold with boundary) with locally finite Hausdorff 2-measure is the Gromov-Hausdorff limit of polyhed…
Metric definition of quasiconformality and exceptional sets
Dimitrios Ntalampekos
We show that a homeomorphism of Euclidean space is quasiconformal if and only if at each point there exists a sequence of uncentered open sets with bounded eccentricity shrinking t…
Polyhedral approximation of metric surfaces and applications to uniformization
Dimitrios Ntalampekos, Matthew Romney
We prove that any length metric space homeomorphic to a 2-manifold with boundary, also called a length surface, is the Gromov-Hausdorff limit of polyhedral surfaces with controlled…
Extension of boundary homeomorphisms to mappings of finite distortion
Christina Karafyllia, Dimitrios Ntalampekos
We provide sufficient conditions so that a homeomorphism of the real line or of the circle admits an extension to a mapping of finite distortion in the upper half-plane or the disk…
On the Hausdorff dimension of the residual set of a packing by smooth curves
Steven Maio, Dimitrios Ntalampekos
Let a planar residual set be a set obtained by removing countably many disjoint topological disks from an open set in the plane. We prove that the residual set of a planar packing…
Monotone Sobolev functions in planar domains: level sets and smooth approximation
Dimitrios Ntalampekos
We prove that almost every level set of a Sobolev function in a planar domain consists of points, Jordan curves, or homeomorphic copies of an interval. For monotone Sobolev functio…
Non-removability of Sierpinski spaces
Dimitrios Ntalampekos, Jang-Mei Wu
We prove that all Sierpiński spaces in , , are non-removable for (quasi)conformal maps, generalizing the result of the first named author arXiv:1809.05605.…
On the inverse absolute continuity of quasiconformal mappings on hypersurfaces
Dimitrios Ntalampekos, Matthew Romney
We construct quasiconformal mappings for which there is a Borel set of positive Lebesgue $…
Non-removability of Sierpinski carpets
Dimitrios Ntalampekos
We prove that all Sierpiński carpets in the plane are non-removable for (quasi)conformal maps. More precisely, we show that for any two Sierpiński carpets $S,S'\subset \hat{\mathbb…
Rigidity theorems for circle domains
Dimitrios Ntalampekos, Malik Younsi
A circle domain in the Riemann sphere is conformally rigid if every conformal map from onto another circle domain is the restriction of a Möbius transformation. We show tha…
Potential theory on Sierpinski carpets with applications to uniformization
Dimitrios Ntalampekos
This research is motivated by the study of the geometry of fractal sets and is focused on uniformization problems: transformation of sets to canonical sets, using maps that preserv…
Non-removability of the Sierpinski Gasket
Dimitrios Ntalampekos
We prove that the Sierpiński gasket is non-removable for quasiconformal maps, thus answering a question of Bishop. The proof involves a new technique of constructing an exceptional…
A removability theorem for Sobolev functions and detour sets
Dimitrios Ntalampekos
We study the removability of compact sets for continuous Sobolev functions. In particular, we focus on sets with infinitely many complementary components, called "detour sets", whi…
Semi-hyperbolic rational maps and size of Fatou components
Dimitrios Ntalampekos
Recently Merenkov and Sabitova introduced the notion of a homogeneous planar set. Using this notion they proved a result for Sierpiski carpet Julia sets of hyperbolic rational…