# Finnur Larusson: The Gauss map and the h-principle

V torek, 4. junija ob 12. uri in 30 minut, bo v okviru seminarja za kompleksno analizo predaval prof. Finnur Larusson z Univerze v Adelaide, Avstralija.

Title: The Gauss map and the h-principle.

Abstract: The Gauss map of a minimal surface in R^3, parametrised as a conformal minimal immersion from an open Riemann surface M into R^3, is a meromorphic function on M. Although the Gauss map has been a central object of interest in the theory of minimal surfaces since the mid-19th century, it was only recently proved by Alarcon, Forstneric and Lopez, using new complex-analytic methods, that every meromorphic function on M is a Gauss map. It remains an open problem to usefully characterise those meromorphic functions that are the Gauss map of a complete minimal surface. I will describe recent joint work with Antonio Alarcon, in which we take a new approach to this problem. We investigate the space of meromorphic functions on M that are the Gauss map of a complete minimal surface from a homotopy-theoretic viewpoint, using a new h-principle as a key tool. My talk will include a brief general introduction to h-principles and their applications.

Predavanje bo potekalo hibridno, v predavalnici 3.06 na Jadranski 21 in preko aplikacije ZOOM:

https://uni-lj-si.zoom.us/j/93098854181

Meeting ID: 930 9885 4181

Vljudno vabljeni!

Vodji seminarja

Franc Forstneric in Barbara Drinovec Drnovsek