Genus 1 minimal k-noids and saddle towers in H-2 x R
Metadatos
Afficher la notice complèteAuteur
Castro Infantes, JesúsEditorial
Cambridge University Press
Materia
Minimal surfaces Finite total curvature Minimal k-noids Saddle towers Conjugate construction
Date
2022-01-06Referencia bibliográfica
Castro-Infantes, J., & Manzano, J. (2022). GENUS 1 MINIMAL k-NOIDS AND SADDLE TOWERS IN H-2 x R. Journal of the Institute of Mathematics of Jussieu, 1-21. doi:[10.1017/S1474748021000591]
Patrocinador
Spanish Government MTM2017-89677-P MCIN/AEI project PID2019-111531GA-I00 PID2020-117868GB-I00; FPU programme from MICINN; EBM/FEDER UJA 2020 project 1380860Résumé
For each k >= 3, we construct a 1-parameter family of complete properly Alexandrov-embedded minimal surfaces in the Riemannian product space H-2 x R with genus 1 and k embedded ends asymptotic to vertical planes. We also obtain complete minimal surfaces with genus 1 and 2k ends in the quotient of H-2 x R by an arbitrary vertical translation. They all have dihedral symmetry with respect to k vertical planes, as well as finite total curvature -4k pi. Finally, we provide examples of complete properly Alexandrov-embedded minimal surfaces with finite total curvature with genus 1 in quotients of H-2 x R by the action of a hyperbolic or parabolic translation.