Orbifold compactness for spaces of Riemannian metrics and applications

Details Orbifold compactness for spaces of Riemannian metrics and applications Orbifold compactness for spaces of Riemannian metrics and applications

2003-12-04

arxiv.org/abs/math/0312111v2

Mathematics

Differential Geometry

28pp. Exposition improved, references added

Scientific paper

This work proves certain general orbifold compactness results for spaces of Riemannian metrics, generalizing earlier results along these lines for Einstein metrics or metrics with bounded Ricci curvature. This is then applied to prove such compactness for spaces of Bach-flat (for example half-conformally flat) metrics on 4-manifolds, and related results for metrics which are critical points of other natural Riemannian functionals on the space of metrics.

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