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Extremal metrics and lower bound of the modified K-energy

Yuji Sano;  Carl Tipler — 2015

Journal of the European Mathematical Society

We provide a new proof of a result of X.X. Chen and G.Tian [5]: for a polarized extremal Kähler manifold, the minimum of the modified K-energy is attained at an extremal metric. The proof uses an idea of C. Li [16] adapted to the extremal metrics using some weighted balanced metrics.

An example of an asymptotically Chow unstable manifold with constant scalar curvature

Hajime Ono;  Yuji Sano;  Naoto Yotsutani — 2012

Annales de l’institut Fourier

Donaldson proved that if a polarized manifold ( V , L ) has constant scalar curvature Kähler metrics in c 1 ( L ) and its automorphism group Aut ( V , L ) is discrete, ( V , L ) is asymptotically Chow stable. In this paper, we shall show an example which implies that the above result does not hold in the case where Aut ( V , L ) is not discrete.

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