Kang-Tae Kim 
Robin Functions for Complex Manifolds and Applications [PDF ebook] 

In a previous Memoirs (Vol. 92, No. 448), Levenberg and Yamaguchi analyzed the second variation of the Robin function $-/lambda(t)$ associated to a smooth variation of domains in $/mathbb{C}^n$ for $n/geq 2$. In the current work, the authors study a generalization of this second variation formula to complex manifolds $M$ equipped with a Hermitian metric $ds^2$ and a smooth, nonnegative function $c$.