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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 220
Hyperelliptic Riemann surfaces of infinite genus and solutionsof the KdV equation W. Müller, M. U. Schmidt, R. Schrader
In this article we construct (connected) hyperelliptic Riemann surfaces of infinite genus which have period matrices close to the diagonal matrix $sqrt{-1}{hbox{diag}( au_1, au_2,cdots)}$ with arbitrary $ au_i>0.$ By previous results of the authors, one may therefore associate (renormalized) theta functions to these surfaces. Via an Its--Matveev formula this gives, in particular, rise to new solutions of the KdV equations
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