# Every meromorphic function is the Gauss map of a conformal minimal surface

## Univerza v Ljubljani

We prove that every meromorphic function on an open Riemann surface \(M\) is the complex Gauss map of a conformal minimal immersion \(f:M\to \mathbb R^3\); furthermore, \(f\) may be chosen as the real part of a holomorphic null curve \(F:M\to\mathbb C^3\). Analogous results are proved for conformal minimal immersions \(M\to\mathbb R^n\) for any \(n>3\). We also show that every conformal minimal immersion \(M\to\mathbb R^n\) is isotopic to a flat one, and we identify the path connected components of the space of all conformal minimal immersions \(M\to\mathbb R^n\) for any \(n\ge 3\). (Joint work with Antonio Alarcón and Francisco J. López,