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Feng Luo - An introduction to discrete conformal geometry of polyhedral surfaces (Part 4)
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Descriptif
The goal of the course is to introduce some of the recent developments on discrete conformal geometry of polyhedral surfaces. We plan to cover the following topics.
- The Andreev-Koebe-Thurston theorem on circle packing polyhedral metrics and Marden-Rodin’s proof
- Thurston’s conjecture on the convergence of circle packings to the Riemann mapping and its solution by Rodin-Sullivan
- Finite dimensional variational principles associated to polyhedral surfaces
- A discrete conformal equivalence of polyhedral surfaces and its relationship to convex polyhedra in hyperbolic 3-space
- A discrete uniformization theorem for compact polyhedral surfaces
- Convergence of discrete conformality and some open problems
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