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# Mathematical Research Letters

## Volume 12 (2005)

### Number 1

### A note on the uniformization of gradient Kähler Ricci solitons

Pages: 19 – 21

DOI: http://dx.doi.org/10.4310/MRL.2005.v12.n1.a2

#### Authors

#### Abstract

Applying a well known result for attracting fixed points of biholomorphisms \cite{RR, V}, we observe that one immediately obtains the following result: if $(M^n,g)$ is a complete non-compact gradient Kähler-Ricci soliton which is either steady with positive Ricci curvature so that the scalar curvature attains its maximum at some point, or expanding with non-negative Ricci curvature, then $M$ is biholomorphic to ${\mathbb C}^n$.