The conformal structure of Riemann surfaces with boundary parametrizing minimal surfaces |
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Authors: | Prof Dr Reinhold Böhme |
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Institution: | (1) Mathematisches Institut der RUB, Universitätsstr. 150, D-4630 Bochum 1 |
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Abstract: | Let F denote a surface with boundary F, being contained in a Riemann surface R, such that R\F is somedisk. If we vary the boiundary curve o parametrizing F, we will get a manifold of real dimension 6g–3, such that any bounds some F and any local deformation
of F is conformally equivalent to just one F for .This result also implies that none of the conformal invariants of R will be an invariant of this F, since its neighbors {F|} cover all possible deformations of F at all. |
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