Seminario di Analisi Complessa

Dipartimento di Matematica

Università di Roma Tor Vergata

Organizzatori: Filippo Bracci , Leandro Arosio

Prossimi seminari:

Tjaša Vrhovnik, University of Granada. Every nonflat conformal minimal surface is homotopic to a proper one

Martedì 30 Settembre 2025 ore 16:00 aula D'Antoni

Abstract: Given an open Riemann surface $M$, we prove that every nonflat conformal minimal immersion $M\to\R^n$ ($n\geq 3$) is homotopic through nonflat conformal minimal immersions $M\to\R^n$ to a proper one. If $n\geq5$, it may be chosen in addition injective, hence a proper conformal minimal embedding. Prescribing its flux, as a consequence, every nonflat conformal minimal immersion $M\to\R^n$ is homotopic to the real part of a proper holomorphic null embedding $M\to\C^n$. We also obtain a result for a more general family of holomorphic immersions from an open Riemann surface into $\C^n$ directed by Oka cones in $\C^n$.