On Properly Embedded Minimal Surfaces with Three Ends
نویسنده
چکیده
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-HoffmanMeeks 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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