2012/10/27 by Hong Huang, Huang, Hong
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG
paper · pdf · doi:10.48550/arxiv.1210.7331
10 pages. arXiv admin note: substantial text overlap with arXiv:0912.5405, arXiv:1107.1469, arXiv:1108.2918
arxiv created 2012/10/27 · arxiv updated 2012/10/30
We prove the following result: Let (O,g0) be a complete, connected 3-orbifold with uniformly positive scalar curvature, with bounded geometry, and containing no bad 2-suborbifolds. Then there is a finite collection F of spherical 3-orbifolds, such that O is diffeomorphic to a (possibly infinite) orbifold connected sum of copies of members in F. This extends work of Perelman and Bessi\graveeres-Besson-Maillot. The proof uses Ricci flow with surgery on complete 3-orbifolds, and are along the lines of the author's previous work on 4-orbifolds with positive isotropic curvature.