Journal:To appear in Commun. Contemp. Math.
Key Words:Generalized circle patterns; Existence; Combinatorial curvature flow
Abstract:In [4], Guo-Luo generalized Bobenko-Springborn’s hyperbolic circle patterns on closed surfaces to surfaces with boundary, and proved its rigidity. In this paper, we prove the existence of Guo-Luo’s generalized circle patterns with prescribed combinatorial curvatures on surfaces with boundary by the continuity method. This result provides a partial answer to a question posed by Guo-Luo in [4]. Furthermore, we introduce two combinatorial curvature
flows associated with these generalized circle patterns on surfaces with boundary, and prove the long-time existence and convergence of the solutions to these combinatorial curvature flows.
Indexed by:Journal paper
Translation or Not:no