Conformal tilings, combinatorial curvature, and the type problem

Planar graphs; geometric and topological aspects of graph theory (05C10) Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45) Rigidity and flexibility of structures (aspects of discrete geometry) (52C25) Tilings in (2) dimensions (aspects of discrete geometry) (52C20) Polyhedral manifolds (52B70) Circle packings and discrete conformal geometry (52C26)

Cites Work

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Strong isoperimetric inequalities and combinatorial curvatures on multiply connected planar graphs
Circle packings in different geometries
Regular tessellations of surfaces and (p,q,2)-triangle groups
A combinatorial analogue of a theorem of Myers
Correction to my paper 'A combinatorial analogue of a theorem of Myers'
Hyperbolic and parabolic packings
On the largest planar graphs with everywhere positive combinatorial curvature
On the number of vertices of positively curved planar graphs
Dessins d'Enfants on Riemann Surfaces
Conformal tilings I: foundations, theory, and practice
An analogue of the Descartes-Euler formula for infinite graphs and Higuchi’s conjecture
The Gauss-Bonnet formula of polytopal manifolds and the characterization of embedded graphs with nonnegative curvature
Geodesics in Piecewise Linear Manifolds
On Deciding Whether a Surface is Parabolic or Hyperbolic
A note on tilings and strong isoperimetric inequality
A “regular” pentagonal tiling of the plane
Combinatorial curvature for planar graphs
Conformal tilings II: Local isomorphism, hierarchy, and conformal type
Some criteria for circle packing types and combinatorial Gauss-Bonnet Theorem
Aleksandrov surfaces and hyperbolicity
Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu

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