Space of Kähler metrics III--On the lower bound of the Calabi energy and geodesic distance

Details Space of Kähler metrics III--On the lower bound of the Calabi energy and geodesic distance Space of Kähler metrics III--On the lower bound of the Calabi energy and geodesic distance

2006-06-09

arxiv.org/abs/math/0606228v1

Mathematics

Differential Geometry

Scientific paper

In this paper, we first prove a folklore conjecture on a greatest lower bound of the Calabi energy in all K\"ahler manifold. Similar result in algebriac setting was obtained by S. K. Donaldson. Secondly, we give an upper/lower bound estimate of the K energy in terms of the geodesic distance and the Calabi energy. This is used to prove a theorem on convergence of K\"ahler metrics in holomorphic coordinates, with uniform bound on the Ricci curvature and the diameter. Thirdly, we set up a framework for the existence of geodesic rays when an asymptotic direction is given. I

Affiliated with

Also associated with

No associations

Rating

Space of Kähler metrics III--On the lower bound of the Calabi energy and geodesic distance 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 Space of Kähler metrics III--On the lower bound of the Calabi energy and geodesic distance, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Space of Kähler metrics III--On the lower bound of the Calabi energy and geodesic distance will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-410097