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A characterization of linear automorphisms of the Euclidean ball

Hidetaka Hamada, Tatsuhiro Honda (1999)

Annales Polonici Mathematici

Let B be the open unit ball for a norm on n . Let f:B → B be a holomorphic map with f(0) = 0. We consider a condition implying that f is linear on n . Moreover, in the case of the Euclidean ball , we show that f is a linear automorphism of under this condition.

A characterization of proper regular mappings

T. Krasiński, S. Spodzieja (2001)

Annales Polonici Mathematici

Let X, Y be complex affine varieties and f:X → Y a regular mapping. We prove that if dim X ≥ 2 and f is closed in the Zariski topology then f is proper in the classical topology.

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