Displaying similar documents to “Stability of vector bundles and extremal metrics.”

Relative K-stability of extremal metrics

Jacopo Stoppa, Gábor Székelyhidi (2011)

Journal of the European Mathematical Society

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We show that if a polarised manifold admits an extremal metric then it is K-polystable relative to a maximal torus of automorphisms.

Extremal metrics and lower bound of the modified K-energy

Yuji Sano, Carl Tipler (2015)

Journal of the European Mathematical Society

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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.

Kähler-Einstein metrics: Old and New

Daniele Angella, Cristiano Spotti (2017)

Complex Manifolds

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We present classical and recent results on Kähler-Einstein metrics on compact complex manifolds, focusing on existence, obstructions and relations to algebraic geometric notions of stability (K-stability). These are the notes for the SMI course "Kähler-Einstein metrics" given by C.S. in Cortona (Italy), May 2017. The material is not intended to be original.