POLYNOMIAL CONVEXITY OF TEICHMULLER-SPACES

It is well known that finite-dimensional Teichmuller spaces are holomo rphically convex, that is, they are domains of holomorphy. Moreover, t he holomorphic convexity is fulfilled for all Teichmuller spaces in a stronger form: they are complex hyperconvex. In this note we establish that, in fact, finite-dimensional Teichmuller spaces possess a much s tronger convexity property, namely, they are polynomially convex; in o ther words, they are Runge domains. Additionally, some geometric prope rties of Teichmuller spaces are established.