Combinatorial curvature flows on surfaces and 3-dimensional manifolds

Combinatorial Ricci flow was first introduced by Chow and Luo for Thurston’s circle packings on surfaces. It provides effective algorithms for finding polyhedral metrics on surfaces with prescribed singularities. After Chow and Luo’s work, combinatorial curvature flows have been extensively studied for different types of discrete conformal structures on surfaces and 3-dimensional manifolds. In this talk, I will give an introduction of these combinatorial curvature flows, and present some recent progresses on the study of combinatorial curvature flows on surfaces and 3-dimensional manifolds.