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Analysis on some linear sets

Robert Kaufman — 1971

Annales de l'institut Fourier

The note discusses a probabilistic method for constructing “small” sets, with regard to differentiable transformations and to quantitative measures of independence.

Topics on Kronecker sets

Robert Kaufman — 1973

Annales de l'institut Fourier

We obtain three theorems about transformation of sets of multiplicity onto Kronecker sets, by means of functions of various differentiability classes. The same method yields an improved theorem on the union of two Kronecker sets.

Two problems on doubling measures.

Robert KaufmanJang-Mei Wu — 1995

Revista Matemática Iberoamericana

Doubling measures appear in relation to quasiconformal mappings of the unit disk of the complex plane onto itself. Each such map determines a homeomorphism of the unit circle on itself, and the problem arises, which mappings f can occur as boundary mappings?

Smooth quasiregular maps with branching in 𝐑 n

Robert KaufmanJeremy T. TysonJang-Mei Wu — 2005

Publications Mathématiques de l'IHÉS

According to a theorem of Martio, Rickman and Väisälä, all nonconstant C-smooth quasiregular maps in , ≥3, are local homeomorphisms. Bonk and Heinonen proved that the order of smoothness is sharp in . We prove that the order of smoothness is sharp in . For each ≥5 we construct a C-smooth quasiregular map in with nonempty branch set.

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