Semi-continuity of the Diederich–Fornaess and Steinness indices

In this paper, we prove the semi-continuity theorem of Diederich–Fornaess index and Steinness index under a smooth deformation of pseudoconvex domains in Stein manifolds.

Complete Kähler–Einstein Metric on Stein Manifolds With Negative Curvature

We show the existence of complete negative Kähler–Einstein metric on Stein manifolds with holomorphic sectional curvature bounded from above by a negative constant. We prove that any Kähler metrics on such manifolds can be deformed to the complete negative Kähler–Einstein metric using the normalized Kähler–Ricci flow.

Parametric jet interpolation for Stein manifolds with the density property

Given a Stein manifold with the density property, we show that under a suitable topological condition it is possible to prescribe derivatives at a finite number of points to automorphisms depending holomorphically on a Stein parameter. This is an Oka property of the manifold and is related to its holomorphic flexibility.