Polynomial Convexity of Teichmuller Spaces

It is well known that finite-dimensional Teichmüller spacesare holomorphically convex, that is, they are domains of holomorphy.Moreover, the holomorphic convexity is fulfilled for all Teichmüllerspaces in a stronger form: they are complex hyperconvex. In this note we establish that, in fact, finite-dimensionalTeichmüller spaces possess a much stronger convexity property,namely, they are polynomially convex; in other words, they areRunge domains. Additionally, some geometric properties of Teichmüllerspaces are established.