Dimitrios Ntalampekos

collaborators

5 papers

math.CA2019

Monotone Sobolev functions in planar domains: level sets and smooth approximation

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…

math.MG2018

Non-removability of Sierpinski spaces

Dimitrios Ntalampekos, Jang-Mei Wu

We prove that all Sierpiński spaces in $S^{n}$ , $n \geq 2$ , are non-removable for (quasi)conformal maps, generalizing the result of the first named author arXiv:1809.05605.…

math.CV2018

Rigidity theorems for circle domains

Dimitrios Ntalampekos, Malik Younsi

A circle domain $Ω$ in the Riemann sphere is conformally rigid if every conformal map from $Ω$ onto another circle domain is the restriction of a Möbius transformation. We show tha…

math.MG2018

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…

math.MG2018

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…