A calculus for meromorphic currents.
The main purpose of this note is to give a new characterization of the well-known Carleson measure in terms of the integral for functions with their derivatives on the unit ball.
We derive conditions under which a holomorphic mapping of a taut Riemann surface must be an automorphism. This is an analogue involving invariant distances of a result of H. Cartan. Using similar methods we prove an existence result for 1-dimensional holomorphic retracts in a taut complex manifold.
We give a characterization for boundedness of plurisubharmonic functions in the Cegrell class ℱ.
Let B be the open unit ball for a norm on . Let f:B → B be a holomorphic map with f(0) = 0. We consider a condition implying that f is linear on . Moreover, in the case of the Euclidean ball , we show that f is a linear automorphism of under this condition.
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.