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- W1996769092 abstract "We develop Teichmuller theoretical methods to construct new minimal surfaces in $BE^3$ by adding handles and planar ends to existing minimal surfaces in $BE^3$. We exhibit this method on an interesting class of minimal surfaces which are likely to be embedded, and have a low degree Gauss map for their genus; the (Weierstrass data) period problem for these surfaces is of arbitrary dimension. In particular, we exhibit a two-parameter family of complete minimal surfaces in the Euclidean three-space $BE^3$ which generalize the breakthrough minimal surface of C. Costa; these new surfaces are embedded (at least) outside a compact set, and are indexed (roughly) by the number of ends they have and their genus. They have at most eight self-symmetries despite being of arbitrarily large genus, and are interesting for a number of reasons. Moreover, our methods also extend to prove that some natural candidate classes of surfaces cannot be realized as minimal surfaces in $BE^3$. As a result of both aspects of this work, we obtain a classification of a family of surfaces as either realizable or unrealizable as minimal surfaces." @default.
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- W1996769092 date "2002-11-01" @default.
- W1996769092 modified "2023-10-18" @default.
- W1996769092 title "Teichmuller Theory and Handle Addition for Minimal Surfaces" @default.
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- W1996769092 doi "https://doi.org/10.2307/3597281" @default.
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