Extremal metrics and lower bound of the modified K-energy

Yuji Sano; Carl Tipler

Extremal metrics and lower bound of the modified K-energy

Differential Geometry 2013-07-30 v2 Algebraic Geometry

Authors: Yuji Sano , Carl Tipler

Abstract

We provide a new proof of a result of X.X.Chen and G.Tian : for a polarized extremal K\"ahler manifold, an extremal metric attains the minimum of the modified K-energy. The proof uses an idea of C.Li adapted to the extremal metrics using some weighted balanced metrics.

Keywords

extremal metric modified K-energy polarized Kähler manifold weighted balanced metrics calabi flow

Cite

@article{arxiv.1211.5585,
  title  = {Extremal metrics and lower bound of the modified K-energy},
  author = {Yuji Sano and Carl Tipler},
  journal= {arXiv preprint arXiv:1211.5585},
  year   = {2013}
}

Comments

19 pages, few typos corrected. More details are given in some proofs. To be published in JEMS

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