Regularity and convergence of 4-dimensional extremal Kahler metrics

Details Regularity and convergence of 4-dimensional extremal Kahler metrics Regularity and convergence of 4-dimensional extremal Kahler metrics

2011-04-16

arxiv.org/abs/1104.3190v2

Mathematics

Differential Geometry

The paper has been temporarily withdrawn pending some corrections and improvements in format. In particular, some arguments su

Scientific paper

We establish a regularity result for the metric on any 4-dimensional extremal K\"ahler manifold, and a weak compactness theorem on the space of such metrics. Specifically, the sectional curvature at a point is bounded when the quantity $L^2(|\Riem|)$ in a surrounding ball is sufficiently small compared to the pointwise norm of its scalar curvature. Consequently sequences of 4-dimensional extremal K\"ahler metrics with uniformly bounded Calabi energies and scalar curvature have convergent subsequences in the Gromov-Hausdorff topology. Gromov-Hausdorff limits are length spaces with the structure of Riemannian orbifolds away from finitely many point-like singularities of unknown structure.

Affiliated with

Also associated with

No associations

Rating

Regularity and convergence of 4-dimensional extremal 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 Regularity and convergence of 4-dimensional extremal Kahler metrics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Regularity and convergence of 4-dimensional extremal Kahler metrics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-346612