Pekka Pankka

A big Picard theorem for quasiregular mappings into manifolds with many ends

We study quasiregular mappings from a punctured Euclidean ball into n-manifolds with many ends and prove, by using Harnacks inequality, a version of the big Picard theorem.

Sharp exponential integrability for traces of monotone Sobolev functions

We answer a question posed in (12) on exponential integrability of functions of restricted n-energy. We use geomet- ric methods to obtain a sharp exponential integrability result for boundary traces of monotone Sobolev functions defined on the unit ball.

Quasiregular mappings from a punctured ball into compact manifolds

We study quasiregular mappings from a punctured unit ball of the Euclidean n-space into compact manifolds. We show that a quasiregular mapping has a limit in the point of punctuation whenever the dimension of the cohomology ring of the compact manifold exceeds a bound given in terms of the dimension and the distortion constant of the mapping.

Equilibrium measures for uniformly quasiregular dynamics

We establish the existence and fundamental properties of the equilibrium measure in uniformly quasiregular dynamics. We show that a uniformly quasiregular endomorphism

Rigidity of extremal quasiregularly elliptic manifolds

f

Rescaling principle for isolated essential singularities of quasiregular mappings

of degree at least 2 on a closed Riemannian manifold admits an equilibrium measure

Uniform cohomological expansion of uniformly quasiregular mappings: UNIFORM COHOMOLOGICAL EXPANSION

\mu_f

Quasiconformal non-parametrizability of almost smooth spheres

, which is balanced and invariant under

Mappings of finite distortion: Global homeomorphism theorem

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Sharpness of Rickman’s Picard theorem in all dimensions

and non-atomic, and whose support agrees with the Julia set of