Seminario de Geometría: “Every meromorphic map is the Gauss map of a conformal minimal surface”

Seminario Geometría
Título: Every meromorphic map is the Gauss map of a conformal minimal surface
Speaker: Franc Forstneric (Universidad de Liubliana, Eslovenia)
Lugar: Seminario 1ª planta (IEMath-Gr)
Abstract:

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