We show that changing the level curve of a harmonic function with the classical Hadamard variation with a small parameter entails a change in the Dirichlet integral of the function which is quadratic in the parameter. As a corollary, we supplement the well-known theorem of Teichmüller about the sum of moduli of doubly connected domains into which an annulus is subdivided by a continuum that differs little from a concentric circle.

中文翻译：

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Teichmüller 的 Modulsatz 和狄利克雷积分的变体

我们证明，用小参数的经典哈达玛变分改变调和函数的水平曲线会导致函数的狄利克雷积分发生变化，该积分是参数的二次方。作为推论，我们补充了著名的 Teichmüller 定理，该定理涉及双连通域的模量之和，其中一个环被一个与同心圆几乎没有什么不同的连续体细分成。