@misc{10481/112223,
year = {2026},
month = {3},
url = {https://hdl.handle.net/10481/112223},
abstract = {Given an open Riemann surface M, we prove that every nonflat conformal minimal
immersion M → R^n (n ≥ 3) is homotopic through nonflat conformalminimal immersions
M → R^n to a proper one. If n ≥ 5, 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 → R^n is homotopic to the real part of a
proper holomorphic null embedding M → 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.},
organization = {MICIU/AEI/10.13039/501100011033 PID2023-150727NB-I00},
organization = {ERDF/EU, Spain},
organization = {Universidad de Granada/CBUA},
publisher = {Springer Nature},
keywords = {Proper minimal surface},
keywords = {Minimal surfaces},
keywords = {Riemann surface},
keywords = {Null curve},
keywords = {Oka manifold},
keywords = {Directed immersion},
title = {Every Nonflat Conformal Minimal Surface is Homotopic to a Proper One},
doi = {10.1007/s12220-026-02389-x},
author = {Vrhovnik, Tjaša},
}