Discrete uniformization problem for polyhedral surfaces
Discrete uniformization problem for polyhedral surfaces
-
Feng Luo, Rutgers University
*Note day and location*
The classical uniformization theorem for Riemann surfaces is well-established for both compact and non-compact connected surfaces. However,听 in the discrete setting, the discrete uniformization theorem is only known for closed polyhedral surfaces. 听This talk will propose a discrete uniformization problem for all surfaces and relate it to the classical Weyl problem in the hyperbolic 3-space and the Cauchy-Alexandrov rigidity theorem on convex polytopes. 听Some of our progress will be discussed,听 including a discrete Schwarz-Pick-Ahlfors lemma and its application. 听This is joint work with Yanwen Luo.