Limit of Karcher's Saddle towers
| dc.creator | Rodriguez, M. Magdalena | |
| dc.date | 2006-11-21 | |
| dc.date | 2006-12-05 | |
| dc.date.accessioned | 2026-07-07T07:33:12Z | |
| dc.date.available | 2026-07-07T07:33:12Z | |
| dc.description | In 1988, Karcher generalized the family of singly periodic Scherk minimal surfaces by constructing, for each natural $n\geq 2$, a $(2n-3)$-parameter family of singly periodic minimal surfaces with genus zero and $2n$ Scherk-type ends in the quotient, called {\it saddle towers}. They have been recently classified by Pérez and Traizet \cite{PeTra1} as the only properly embedded singly periodic minimal surfaces in $\R^3$ with genus zero and finitely many Scherk-type ends in the quotient. In this paper we obtain as a limit of saddle towers: the catenoid; the doubly periodic Scherk minimal surface of angle $\fracπ{2}$; any singly periodic Scherk minimal surface; or a KMR example of the kind $M_{\t,\a,0}$ (also called {\it toroidal halfplane layer}, see \cite{ka4,mrod1}), which are doubly periodic minimal surfaces with parallel ends and genus one in the quotient; or one of the examples constructed in \cite{mrt}, which are singly periodic minimal surfaces with genus zero and one limit end in the quotient by all their periods. | |
| dc.description | 8 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0611654 | |
| dc.identifier | http://arxiv.org/abs/math/0611654 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119372 | |
| dc.subject | Differential Geometry | |
| dc.subject | 49Q05; 53A10 | |
| dc.title | Limit of Karcher's Saddle towers | |
| dc.type | text |