We extend existing methods which treat the semilinear Calderón problem on a bounded domain to a class of complex manifolds with Kähler metric. Given two semilinear Schrödinger operators with the same Dirchlet-to-Neumann data, we show that the integral identities that appear naturally in the determination of the analytic potentials are enough to deduce uniqueness on the boundary up to infinite order. By exploiting the assumed complex structure, this information allows us to apply the method of stationary phase and recover the potentials in the interior as well.

中文翻译：

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使用 KÄHLER 公制的 STEIN 歧管上的半线性 CALDERÓN 问题

我们将处理有界域上的半线性 Calderón 问题的现有方法扩展到具有 Kähler 度量的一类复杂流形。给定两个具有相同 Dirchlet-to-Neumann 数据的半线性薛定谔算子，我们表明，在确定解析势时自然出现的积分恒等式足以推断出边界上的唯一性，直至无限阶。通过利用假设的复杂结构，这些信息使我们能够应用固定相的方法并恢复内部的电位。