7 papers
A prescribed curvature flow on hyperbolic surfaces with infinite topological type
Xinrong Zhao, Puchun Zhou
In this paper, we investigate the prescribed total geodesic curvature problem for generalized circle packing metrics in hyperbolic background geometry on surfaces with infinite cel…
Convergences of Combinatorial Ricci Flows to Degenerated Circle Packings in Hyperbolic Background Geometry
Guangming Hu, Sicheng Lu, Dong Tan +2
This paper investigates a kind of degenerated circle packings in hyperbolic background geometry. A main problem is whether a prescribed total geodesic curvature data can be realize…
The Convergence of Prescribed Combinatorial Ricci Flows for Total Geodesic Curvatures in Spherical Background Geometry
Guangming Hu, Ziping Lei, Yu Sun +1
In this paper, we study the existence and rigidity of (degenerated) circle pattern metric with prescribed total geodesic curvatures in spherical background geometry. To find the (d…
Combinatorial p-th Calabi Flows for Total Geodesic Curvatures in hyperbolic background geometry
Guangming Hu, Ziping Lei, Yi Qi +1
In hyperbolic background geometry, we investigate a generalized circle packing (including circles, horocycles and hypercycles) with conical singularities on a surface with boundary…
Hyperbolic Circle Packings and Total Geodesic Curvatures on Surfaces with Boundary
Guangming Hu, Yi Qi, Yu Sun +1
This paper investigates a generalized hyperbolic circle packing (including circles, horocycles or hypercycles) with respect to the total geodesic curvatures on the surface with bou…
Combinatorial Calabi flows for ideal circle patterns in spherical background geometry
Ziping Lei, Puchun Zhou
Combinatorial Calabi flows are introduced by Ge in his Ph.D. thesis (Combinatorial methods and geometric equations, Peking University, Beijing, 2012), and have been studied extensi…
A combinatorial curvature flow in spherical background geometry
Huabin Ge, Bobo Hua, Puchun Zhou
In [12], the existence of ideal circle patterns in Euclidean or hyperbolic background geometry under the combinatorial conditions was proved using flow approaches. It remains as an…