Extremal Kähler metrics and energy functionals on projective bundles

In this article, we prove the equivalence of the existence of extremal Kähler metrics and the properness of the modified K -energy on projective bundles. Moreover, we discuss the relations of the lower boundedness of the K -energy, the infimum of the Calabi energy and the extremal polynomials. In pa...

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Published in:Annals of global analysis and geometry 2012-04, Vol.41 (4), p.423-445
Main Author: Li, Haozhao
Format: Article
Language:English
Subjects:
Analysis
Differential Geometry
Energy
Geometry
Global Analysis and Analysis on Manifolds
Mathematical functions
Mathematical Physics
Mathematics
Mathematics and Statistics
Studies
Topological manifolds
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description In this article, we prove the equivalence of the existence of extremal Kähler metrics and the properness of the modified K -energy on projective bundles. Moreover, we discuss the relations of the lower boundedness of the K -energy, the infimum of the Calabi energy and the extremal polynomials. In particular, the author gives an example where the modified K -energy is bounded from below but not proper.
doi_str_mv 10.1007/s10455-011-9292-y
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subjects Analysis
Differential Geometry
Energy
Geometry
Global Analysis and Analysis on Manifolds
Mathematical functions
Mathematical Physics
Mathematics
Mathematics and Statistics
Studies
Topological manifolds
title Extremal Kähler metrics and energy functionals on projective bundles
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