Analytic polyhedra with non-compact automorphism group

Abstract

The main theme of this article concerns the characterization problem of analytic polyhedra in $\mathbf{C}^n$ with non-compact automorphism group. In particular, we include a proof that every bounded convex analytic polyhedron in $\mathbf{C}^n$ is biholomorphic to the product of a Kobayashi hyperbolic convex cone and a bounded convex domain. Several related recent developments are also introduced.