Discrete uniformization problem for polyhedral surfaces
Discrete uniformization problem for polyhedral surfaces

Feng Luo, Rutgers University
Fine Hall 401
*Note day and location*
The classical uniformization theorem for Riemann surfaces is wellestablished for both compact and noncompact connected surfaces. However, in the discrete setting, the discrete uniformization theorem is only known for closed polyhedral surfaces. This talk will propose a discrete uniformization problem for all surfaces and relate it to the classical Weyl problem in the hyperbolic 3space and the CauchyAlexandrov rigidity theorem on convex polytopes. Some of our progress will be discussed, including a discrete SchwarzPickAhlfors lemma and its application. This is joint work with Yanwen Luo.