On properly embedded minimal surfaces with three ends
Francisco Martín and Matthias Weber
Source: Duke Math. J. Volume 107, Number 3
(2001), 533-559.
Abstract
We classify all complete embedded minimal surfaces in ℝ3; with three ends of genus g and at least 2g+2 symmetries. The surfaces in this class are the Costa-Hoffman-Meeks surfaces that have 4g+4 symmetries in the case of a flat middle end. The proof consists of using the symmetry assumptions to deduce the possible Weierstrass data and then studying the period problems in all cases. To handle the 1-dimensional period problems, we develop a new general method to prove convexity results for period quotients. The 2-dimensional period problems are reduced to the 1-dimensional case by an extremal length argument.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1091737023
Mathematical Reviews number (MathSciNet): MR1828301
Digital Object Identifier: doi:10.1215/S0012-7094-01-10735-7
Zentralblatt MATH identifier: 1044.53006
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