A lower bound for the Kähler-Einstein distance from the Diederich-Fornæss index

Abstract

In this note we establish a lower bound for the distance induced by the Kähler-Einstein metric on pseudoconvex domains with positive hyperconvexity index (e.g. positive Diederich-Fornaess index). A key step is proving an analog of the Hopf lemma for Riemannian manifolds with Ricci curvature bounded from below.

6 pages. Comments very welcome. v3: slight improvement in main result