Robin functions for complex manifolds and applications

Details Robin functions for complex manifolds and applications Robin functions for complex manifolds and applications

2007-10-10

arxiv.org/abs/0710.1901v1

Mathematics

Complex Variables

126 pages, 2 figures

Scientific paper

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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