17 citations · 23 across the 4 of their papers we have counts for
5 papers · 1 filter
Analytic capacity and holomorphic motions
Stamatis Pouliasis, Thomas Ransford, Malik Younsi
We study the behavior of the analytic capacity of a compact set under deformations obtained by families of conformal maps depending holomorphically on the complex parameter. We sho…
Continuity of capacity of a holomorphic motion
Thomas Ransford, Malik Younsi, Wen-hui Ai
We study the behavior of various set-functions under holomorphic motions. We show that, under such deformations, logarithmic capacity varies continuously, while analytic capacity m…
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…
Analytic Capacity : computation and related problems
Malik Younsi
We present a brief introduction to analytic capacity, with an emphasis on its numerical computation. We also discuss several related open problems.
Removability and non-injectivity of conformal welding
Malik Younsi
We construct a (non-removable) Jordan curve and a non-Möbius homeomorphism of the Riemann sphere which is conformal on the complement of and maps the curve onto itself.…