Curvature and geometry of tessellating plane graphs

Discrete and Computational Geometry

Volumn 25, Issue 1, 2001, Pages 141-159

  Baues, O ^a   Peyerimhoff, N ^b  

^a ETH ZURICH   (Switzerland)

^b RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035585022     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004540010076     Document Type: Article

References (19)

1. W. Ballmann, S. Buyalo, Nonpositively curved metrics on 2-polyhedra, Math. Z. 222 (1996), 97-134.
2. P. L. Bowers, Negatively curved graph and planar metrics with applications to type, Michigan Math. J. 45 (1998), 31-53.
3. A. Dress, D. Huson, On tilings of the plane, Geom. Dedicata 24 (1987), 295-310.
4. J. Dodziuk, Difference equations, isoperimetric inequalities and transience of certain random walks, Trans. Amer. Math. Soc. 284 (1984), 787-794.
5. K. Fujiwara, Growth and the spectrum of the Laplacian of an infinite graph, Tôhoku Math. J. 48 (1996), 293-302.
6. E. Ghys, A. Haefliger, A. Verjovsky, Group Theory from a Geometrical Viewpoint, World Scientific, Singapore, 1991.
7. V. W. Guillemin, A. Pollack, Differentiable Topology, Prentice-Hall, Englewood Cliffs, NJ, 1974.
8. B. Grünbaum, G. Shephard, Tilings and Patterns, Freeman, New York, 1987.
9. P. Li, Complete surfaces of at most quadratic area growth, Comment. Math. Helv. 72 (1997), 67-71.
10. R. C. Lyndon, On Dehn's algorithm, Math. Ann. 166 (1966), 208-228.
11. G. Pólya, An elementary analogue to the Gauß-Bonnet theorem, Amer. Math. Monthly 61 (1954), 601-603.
12. S. Rogmann, Wachstumsfunktionen von Pflasterungen, Diplomarbeit, Heinrich-Heine-Universität Düsseldorf, 1997.
13. P. M. Soardi, Recurrence and transience of the edge graph of a tiling of the Euclidean plane, Math. Ann. 287 (1990), 613-626.
14. C. Thomassen, Planarity and duality of finite and infinite graphs, J. Combin. Theory Ser. B 29 (1980), 244-271.
15. W. P. Thurston, Shapes of polyhedra and triangulations of the sphere, in I. Rivin et al. (eds.): The Epstein Birthday Schrift, Geom. Topol. Monogr. 1, Warwick, Coventry, 1998, pp. 511-549.
16. A. T. White, Graphs, Groups and Surfaces, revised edition, Mathematics Studies 8, North-Holland, Amsterdam, 1984.
17. W. Woess, A note on tilings and strong isoperimetric inequality, Math. Proc. Cambridge Philos. Soc. 124 (1998), 385-393.
18. J. W. T. Youngs, Minimal embeddings and the genus of a graph, J. Math. Mech. 12 (1963), 303-315.
19. A. Żuk, On the norms of the random walks on planar graphs, Ann. Inst. Fourier 41 (1997), 1463-1490.