Energy functionals and canonical Kahler metrics

Details Energy functionals and canonical Kahler metrics Energy functionals and canonical Kahler metrics

2005-05-23

arxiv.org/abs/math/0505476v3

Duke Math. J. 137 (2007), no. 1, 159--184

Mathematics

Differential Geometry

23 pages. Published version

Scientific paper

Yau conjectured that a Fano manifold admits a Kahler-Einstein metric if and only if it is stable in the sense of geometric invariant theory. There has been much progress on this conjecture by Tian, Donaldson and others. The Mabuchi energy functional plays a central role in these ideas. We study the E_k functionals introduced by X.X. Chen and G. Tian which generalize the Mabuchi energy. We show that if a Fano manifold admits a Kahler-Einstein metric then the functional E_1 is bounded from below, and, modulo holomorphic vector fields, is proper. This answers affirmatively a question raised by Chen. We show in fact that E_1 is proper if and only if there exists a Kahler-Einstein metric, giving a new analytic criterion for the existence of this canonical metric, with possible implications for the study of stability. We also show that on a Fano Kahler-Einstein manifold all of the functionals E_k are bounded below on the space of metrics with nonnegative Ricci curvature.

Affiliated with

Also associated with

No associations

Rating

Energy functionals and canonical Kahler metrics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Energy functionals and canonical Kahler metrics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Energy functionals and canonical Kahler metrics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-560089