@misc{10481/107916,
year = {2025},
month = {11},
url = {https://hdl.handle.net/10481/107916},
abstract = {Let M be an open Riemann surface and n ≥ 3 be an integer. In this paper, we
establish some generic properties (in Baire category sense) in the space of all
conformal minimal immersions M → Rn endowed with the compact-open topology,
pointing out that a generic such immersion is chaotic in many ways. For instance, we
show that a generic conformal minimal immersion u: M → Rn is non-proper, almost
proper, and g-complete with respect to any given Riemannian metric g in Rn.
Further, its image u(M) is dense in Rn and disjoint from Q3 × Rn−3
, and has infinite
area, infinite total curvature, and unbounded curvature on every open set in Rn. In
case n = 3, we also prove that a generic conformal minimal immersion M → R3 has
infinite index of stability on every open set in R3.},
organization = {AEI (PID2020-117868GB-I00; PID2023-150727NB-I00)},
organization = {MICIU/AEI/10.13039/501100011033 (CEX2020-001105-M, “María de Maeztu” Excellence Unit IMAG)},
organization = {Universidad de Granada (Open access)},
publisher = {Cambridge University Press},
keywords = {Baire category theorem},
keywords = {completely metrizable space},
keywords = {generic property},
title = {Generic properties of minimal surfaces},
doi = {10.1017/prm.2025.10088},
author = {Alarcón López, Antonio and López Fernández, Francisco José},
}