A discrete uniformization theorem for polyhedral surfaces

A discrete uniformization theorem for polyhedral surfaces

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Feng Luo, Rutgers University
Fine Hall 314

The classical uniformization theorem states that every Riemann surface carries a complete constant curvature Riemannian metric in its conformal class. It is difficult to algorithmically implement the uniformization theorem for polyhedral surfaces. We introduce a notion of discrete conformality for polyhedral surfaces and prove a discrete version of the uniformization theorem for compact polyhedral surfaces. This is a joint work with David Gu, Jian Sun and Tianqi Wu.