ALGEBRAIC-CURVES AND NON RIGID MINIMAL-SURFACES IN THE EUCLIDEAN-SPACE

Using method from algebraic geometry we prove: Theorem. Let X be a com pact connected Riemann surface and Z be a non empty finite subset of X . Then there is a complete minimal immersion F : X - Z --> R-3 such th at F(X - Z) is non rigid and of finite total Gaussian curvature.