Local Collapsing, Orbifolds, and Geometrization

This Volume Has Two Papers, Which Can Be Read Separately. The First Paper Concerns Local Collapsing In Riemannian Geometry. We Prove That A Three-dimensional Compact Riemannian Manifold Which Is Locally Collapsed, With Respect To A Lower Curvature Bound, Is A Graph Manifold. This Theorem Was Stated By Perelman Without Proof And Was Used In His Proof Of The Geometrization Conjecture. The Second Paper Is About The Geometrization Of Orbifolds. A Three-dimensional Closed Orientable Orbifold, Which Has No Bad Suborbifolds, Is Known To Have A Geometric Decomposition From Work Of Perelman In The Manifold Case, Along With Earlier Work Of Boileau-leeb-porti, Boileau-maillot-porti, Boileau-porti, Cooper-hodgson-kerckhoff And Thurston. We Give A New, Logically Independent, Unified Proof Of The Geometrization Of Orbifolds, Using Ricci Flow.--provided By Publisher