科研之友
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摘要
Let phi(z) be holomorphic in the unit disk Delta and meromorphic on Delta. Suppose f is a Teichmuller mapping with complex dilatation kphi/\phi\. In 1968, Sethares conjectured that f is extremal if and only if either (i) phi has a double pole or (ii) phi has no pole of order exceeding two on alphaDelta. The "if" part of the conjecture had been solved by himself. We will give the affirmative answer to the "only if" part of the conjecture. In addition, a more general criterion for extremality of quasiconformal mappings is constructed in this paper, which generalizes the "if" part of Sethares' conjecture and improves the result by Reich and Shapiro in 1990.
- 出版日期2004-4
- 单位北京大学
