Remarks on the metric induced by the Robin function III

Abstract

Let $D$ be a smoothly bounded pseudoconvex domain in ${\mathbf{C}}^n$, $n>1$. Using the Robin function $\Lambda (p)$ that arises from the Green function $G(z,p)$ for $D$ with pole at $p\in D$ associated with the standard sum-of-squares Laplacian, N. Levenberg and H. Yamaguchi had constructed a Kähler metric (the so-called $\Lambda$-metric) on $D$. In this article, we study the existence of geodesic spirals for this metric.

17 pages