@misc{10481/79823,
year = {2023},
month = {1},
url = {https://hdl.handle.net/10481/79823},
abstract = {We generalize the classical Henneberg minimal surface by giving
an infinite family of complete, finitely branched, non-orientable, stable
minimal surfaces in R3. These surfaces can be grouped into subfamilies
depending on a positive integer (called the complexity), which essentially
measures the number of branch points. The classical Henneberg surface
H1 is characterized as the unique example in the subfamily of the simplest
complexity m = 1, while for m ≥ 2 multiparameter families are given.
The isometry group of the most symmetric example Hm with a given
complexity m ∈ N is either isomorphic to the dihedral isometry group
D2m+2 (if m is odd) or to Dm+1 × Z2 (if m is even). Furthermore, for m
even Hm is the unique solution to the Bj¨orling problem for a hypocycloid
of m + 1 cusps (if m is even), while for m odd the conjugate minimal
surface H
∗
m to Hm is the unique solution to the Bj¨orling problem for a
hypocycloid of 2m + 2 cusps.},
organization = {Universidad de Granada/CBUA	CEX2020-001105-M/AEI/10.13039/501100011033},
organization = {Ministry of Science and Innovation, Spain (MICINN)
Spanish Government},
organization = {European Commission	PID2020-117868GB-I00	
Junta de Andalucia	P18-FR-4049	
A-FQM-139-UGR18},
publisher = {Springer},
title = {Generalized Henneberg Stable Minimal Surfaces},
doi = {10.1007/s00025-022-01831-0},
author = {Moya Hinojosa, David and Pérez Muñoz, Joaquín},
}