The geometry of analytic varieties satisfying the local Phragmén-Lindelöf condition and a geometric characterization of the partial differential operators that are surjective on $\mathcal \{A\}(\mathbb \{R\}^4)$

Abstract

The local Phragmen-Lindelof condition for analytic subvarieties of C n at real points plays a crucial role in complex analysis and in the theory of constant coefficient partial differential operators, as Hormander has shown. Here, necessary geometric conditions for this Phragmen-Lindelof condition are derived. They are shown to be sufficient in the case of curves in arbitrary dimension and of surfaces in C 3 . The latter result leads to a geometric characterization of those constant coefficient partial differential operators which are surjective on the space of all real analytic functions on R 4 .