# Geometry Seminar – Franc Forstneric

#### Detalles de Evento

Title: The parametric h-principle for minimal surfaces in $R^n$
and null curves in $C^n$

Speaker: Franc Forstneric (Univerza v Ljubljani)

Abstract: Let M be an open Riemann surface. It was proved by Alarcón and Forstneric that every conformal minimal immersion M→$R^3$ is isotopic to the real part of a holomorphic null curve M→$C^3$. We prove the following substantially stronger result in this direction: for any n≥3, the inclusion of the space of real parts of non flat null holomorphic immersions M→$C^n$ into the space of non flat conformal minimal immersions M→$R^n$ satisfies the parametric h-principle with approximation; in particular, it is a weak homotopy equivalence. Analogous results hold for several other related maps. For an open Riemann surface M of finite topological type, we obtain optimal results by showing that the above inclusion and several related maps are inclusions of strong deformation retracts; in particular, they are homotopy equivalences. (Joint work with Finnur Lárusson.)

18 March 2016, 11:30, 1st floor Seminar room, IEMath-GR