Moduli spaces of critical Riemannian metrics with L^{n/2} norm curvature bounds

Details Moduli spaces of critical Riemannian metrics with L^{n/2} norm curvature bounds Moduli spaces of critical Riemannian metrics with L^{n/2} norm curvature bounds

2007-05-30

arxiv.org/abs/0705.4440v1

Mathematics

Differential Geometry

72 pages

Scientific paper

We consider the moduli space of the extremal K\"ahler metrics on compact manifolds. We show that under the conditions of two-sided total volume bounds, $L^{n\over2}$-norm bounds on $\Riem$, and Sobolev constant bounds, this Moduli space can be compactified by including (reduced) orbifolds with finitely many singularities. Most of our results go through for certain other classes of critical Riemannian metrics.

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