A Characterization of the Unit Ball by a Kähler–Einstein Potential

Abstract

We will show that a universal covering of a compact Kähler manifold with ample canonical bundle is the unit ball if it admits a global potential function of the Kähler–Einstein metric whose gradient length is a minimal constant. As an application, we will extend the Wong–Rosay theorem to a complex manifold without boundary. © 2022, Mathematica Josephina, Inc.