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

Understand

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.