Seminario de Geometría: «Every meromorphic map is the Gauss map of a conformal minimal surface»


Detalles de Evento

  • Inicio: 27 enero 2017 11:30
  • Lugar de encuentro: IEMath-GR
  • Categorías: ,
  • Speaker: Franc Forstneric
  • Institution: Universidad de Liubliana, Eslovenia
  • Organizer: Antonio Alarcón

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)