Extremal metrics and lower bound of the modified K-energy

Abstract

We provide a new proof of a result of X.X.Chen and G.Tian : for a polarized extremal Kähler 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.

arXiv comment19 pages, few typos corrected. More details are given in some proofs. To be published in JEMS

Cited by in corpus (1)

• Complex optimal transport and the pluripotential theory of Kähler-Ricci solitons