Geometrization of Three-Dimensional Orbifolds via Ricci Flow

By Bruce Kleiner, J. Lott. 2011

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A three-dimensional closed orientable orbifold (with no bad suborbifolds) is known to have a geometric decomposition from work of Perelman along with earlier work of Boileau-Leeb-Porti and Cooper-Hodgson-Kerckhoff. We give a new, logically independent, unified proof of the geometrization of orbifolds, using Ricci flow. Along the way we develop some tools for the geometry of orbifolds that may be of independent interest.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/0429fb9872c22e8f0ca5a8379a165010006df0e3