Ricci flow on Poincare' and Thurston's Geometrization Conjecture
Hassan Jolany
TL;DR
This thesis reviews Ricci flow and its role in understanding the Poincaré and Thurston geometrization conjectures, highlighting key estimates and functionals used in the field.
Contribution
It provides a comprehensive overview of Ricci flow techniques and their application to major geometric conjectures, emphasizing Perelman's functionals and estimates.
Findings
Summarizes Ricci flow's application to the Poincaré conjecture
Highlights Perelman's functionals and estimates
Reviews key principles like maximum principle and non-collapsing
Abstract
In this thesis we give a review on Ricci flow, an overview on Poincare conjecture, maximum principle, Li-Yau-Perelman estimate, Two functional F and W of Perelman, Reduced volume and reduced length and k-non collapsing estimate
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Mathematical Dynamics and Fractals