The object of the paper is to show that if f is a univalent, harmonic mapping of the annulus A(r, 1) = {z:r < |z| < 1} onto the annulus A(R, 1), and if s is the length of the segment of the Grotzsch ring domain associated with A(r, 1), then R < s. This gives the first, quantitative upper bound of R, which relates to a question of J. C. C. Nitsche that he raised in 1962. The question of whether this bound is sharp remains open.
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机译：本文的目的是表明，如果f为单价，则环A（r，1）= {z：r <| z | <1}到环A（R，1）上，如果s是与A（r，1）关联的格罗茨奇环域的片段的长度，则R 展开▼
