2 papers
math.GT2023
Boundary metric of Epstein-Penner convex hull and discrete conformality
Xin Nie
The Epstein-Penner convex hull construction associates to every decorated punctured hyperbolic surface a polyhedral convex body in the Minkowski space. It works in the de Sitter an…
math.DG2023
On circle patterns and spherical conical metrics
Xin Nie
The Koebe-Andreev-Thurston circle packing theorem, as well as its generalization to circle patterns due to Bobenko and Springborn, holds for Euclidean and hyperbolic metrics possib…