The space of Kähler potentials on an asymptotically locally euclidean Kähler manifold

2013/11/03 by Aleyasin, S. Ali
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1311.0419

Abstract

In this note, we shall prove geodesic convexity of the space of Kähler potentials on an ALE Kähler manifold. This extends earlier results in the compact case proved in the fundamental work of X-X. Chen. We further prove the boundedness from below of the Mabuchi energy, and give an alternative proof for the uniqueness of scalar-flat metrics in the category of ALE Kähler manifold.

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