Some Convexity Features Associated with Unitary Orbits

Let V be an analytic variety in some open set in Cn which contains the origin and which is purely k-dimensional. For a curve gamma in Cn, defined by a convergent Puiseux series and satisfying gamma(0) = 0, and d > 1, define Vt := t^-d ( V - gamma (t) ). Then the currents defined by Vt converge to a limit current Tgamma,d [V] as t tends to zero. Tgamma,d [V] is either zero or its support is an algebraic variety of pure dimension k in Cn. Properties of such limit currents and examples are presented. These results will be applied in a forthcoming paper to derive necessary conditions for varieties satisfying the local Phragmén-Lindel?f condition that was used by H?rmander to characterize the constant coefficient partial differential operators which act surjectively on the space of all real analytic functions on Rn.