Genus one minimal k-noids and saddle towers in $\mathbb{H}^2\times\mathbb{R}$
| Autor: | Castro-Infantes, Jesús, Manzano, José M. |
|---|---|
| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Journal of the Instute of Mathematics of Jussieu 22 (2023), no. 5, 2155-2175 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1017/S1474748021000591 |
| Popis: | For each $k\geq 3$, we construct a 1-parameter family of complete properly Alexandrov-embedded minimal surfaces in the Riemannian product space $\mathbb{H}^2\times\mathbb{R}$ 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 $\mathbb{H}^2\times\mathbb{R}$ 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 also provide examples of complete properly Alexandrov-embedded minimal surfaces with finite total curvature with genus $1$ in quotients of $\mathbb{H}^2\times\mathbb{R}$ by the action of a hyperbolic or parabolic translation. Comment: 19 pages, 8 figures. In this revised version, we have expanded the preliminaries, changed the figures, and made other changes related to the presentation of the manuscript |
| Databáze: | arXiv |
| Externí odkaz: |
|