17 citations · 45 across the 14 of their papers we have counts for
22 papers
A holomorphic motion with non-subharmonic Hausdorff dimension
Thomas Ransford, Malik Younsi
We present an example of a holomorphic motion of a Cantor set for which neither the Hausdorff dimension $\dimH(A_λ)$ nor the lower Minkowski dimension $\dimMl(A_λ)$…
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…
Holomorphic motions, Assouad dimension and quasiconformal mappings
Katheryn Menssen, Malik Younsi
We study the variation of the quasi-Assouad dimension of a set moving under a holomorphic motion. We show that the reciprocal of the quasi-Assouad dimension is inf-harmonic in the…
Rational lemniscates and the matching problem
Kirill Lazebnik, Pierre-Olivier Parisé, Malik Younsi
The matching problem for a given Jordan curve in the complex plane asks to find two nonconstant functions, one analytic in the bounded complementary component of the curve and the…
Holomorphic motions, dimension, area and quasiconformal mappings
Aidan Fuhrer, Thomas Ransford, Malik Younsi
We describe the variation of the Minkowski, packing and Hausdorff dimensions of a set moving under a holomorphic motion, as well as the variation of its area. Our method provides a…
Continuous analytic capacity and holomorphic motions
Malik Younsi
We construct a compact set whose continuous analytic capacity does not vary continuously under a certain holomorphic motion, thereby answering a question of Paul Gauthier. Our exam…
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…
Computing polynomial conformal models for low-degree Blaschke products
Trevor Richards, Malik Younsi
For any finite Blaschke product , there is an injective analytic map and a polynomial of the same degree as such that on $\mathbb…
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.…
Fekete polynomials and shapes of Julia sets
Kathryn A. Lindsey, Malik Younsi
We prove that a nonempty, proper subset of the complex plane can be approximated in a strong sense by polynomial filled Julia sets if and only if is bounded and $\hat{\math…
Removability, rigidity of circle domains and Koebe's Conjecture
Malik Younsi
A circle domain in the Riemann sphere is conformally rigid if every conformal map of onto another circle domain is the restriction of a Möbius transformation. We show that…
Conformal models and fingerprints of pseudo-lemniscates
Trevor Richards, Malik Younsi
We prove that every function that is meromorphic on the closure of an analytic Jordan domain and sufficiently well-behaved on the boundary is conformally equivalent to a rational m…
On removable sets for holomorphic functions
Malik Younsi
We present a comprehensive survey on removability of compact plane sets with respect to various classes of holomorphic functions. We also discuss some applications and several open…
On the analytic and Cauchy capacities
Malik Younsi
We give new sufficient conditions for a compact set to satisfy , where is the analytic capacity and is the Cauchy capacity. As a con…
Shapes, fingerprints and rational lemniscates
Malik Younsi
It has been known since the work of A.A. Kirillov that any smooth Jordan curve in the plane can be represented by its so-called fingerprint, an orientation preserving smooth diffeo…
Finitely connected domains, Rational maps and Ahlfors functions
Maxime Fortier Bourque, Malik Younsi
Using Ahlfors functions, Grunsky maps and the Bell representation theorem, we show that a certain subset of the rational maps of degree forms a trivial bundle over the moduli s…
Rational Ahlfors Functions
Maxime Fortier Bourque, Malik Younsi
We study a problem of Jeong and Taniguchi asking to find all rational maps which are Ahlfors functions. We prove that the rational Ahlfors functions of degree two are characterized…
Proof of a Combinatorial Conjecture Coming from the PAC-Bayesian Machine Learning Theory
Malik Younsi
We give a proof of a conjecture of A. Lacasse in his doctoral thesis which has applications in machine learning algorithms. The proof relies on some interesting binomial sums ident…
Computation of Analytic Capacity and applications to the Subadditivity Problem
Malik Younsi, Thomas Ransford
We develop a least-squares method for computing the analytic capacity of compact plane sets with piecewise-analytic boundary. The method furnishes rigorous upper and lower bounds w…