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arXiv · 0705.4440

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

Xiuxiong Chen·Brian Weber
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Abstract

We consider the moduli space of the extremal Kähler 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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Xiuxiong Chen, Brian Weber. 2007-05-30. Moduli spaces of critical Riemannian metrics with L^{n/2} norm curvature bounds. https://arxiv.org/abs/0705.4440

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