复流形上的Robin函数及其应用
Robin functions for complex manifolds and applications
摘要：
我们证明了C^N中与区域光滑变分相关联的Robin函数的二阶变分公式到与复流形M中的区域光滑变分相关联的c-Robin函数的情形的推广，M具有Hermitian度量和光滑非负函数c。我们的目的是，与此增加的灵活性，我们能够给出一个标准的有界，光滑有界，伪凸域D在一个复杂的齐性空间是斯坦。
英文摘要：
We prove a generalization of the second variation formula of the Robin function associated to a smooth variation of domains in C^N to the case of the c-Robin function associated to a smooth variation of domains in a complex manifold M equipped with a Hermitian metric and a smooth, nonnegative function c. Our purpose is that, with this added flexibility, we are able to give a criterion for a bounded, smoothly bounded, pseudoconvex domain D in a complex homogeneous space to be Stein.
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