Geodesic
The centered dual and the maximal injectivity radius of hyperbolic surfaces
DeBlois, Jason1
1 Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA 15260, USA
Geometry & topology, Tome 19 (2015) no. 2, pp. 953-1014.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We give sharp upper bounds on the maximal injectivity radius of finite-area hyperbolic surfaces and use them, for each g ≥ 2, to identify a constant rg−1,2 such that the set of closed genus-g hyperbolic surfaces with maximal injectivity radius at least r is compact if and only if r > rg−1,2. The main tool is a version of the centered dual complex that we introduced earlier, a coarsening of the Delaunay complex. In particular, we bound the area of a compact centered dual two-cell below given lower bounds on its side lengths.

DOI : 10.2140/gt.2015.19.953
Classification : 52C15, 57M50
Keywords: hyperbolic surface, injectivity radius, packing, Delaunay

DeBlois, Jason 1

1 Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA 15260, USA 
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DeBlois, Jason. The centered dual and the maximal injectivity radius of hyperbolic surfaces. Geometry & topology, Tome 19 (2015) no. 2, pp. 953-1014. doi : 10.2140/gt.2015.19.953. http://geodesic.mathdoc.fr/articles/10.2140/gt.2015.19.953/

[1] C Bavard, Disques extrémaux et surfaces modulaires, Ann. Fac. Sci. Toulouse Math. 5 (1996) 191

[2] R Benedetti, C Petronio, Lectures on hyperbolic geometry, Springer (1992)

[3] K Böröczky, Packing of spheres in spaces of constant curvature, Acta Math. Acad. Sci. Hungar. 32 (1978) 243

[4] J A De Loera, J Rambau, F Santos, Triangulations: Structures for algorithms and applications, Algorithms and Computation in Mathematics 25, Springer (2010)

[5] J Deblois, The Delaunay tessellation in hyperbolic space,

[6] J Deblois, Tessellations of hyperbolic surfaces,

[7] J Deblois, The geometry of cyclic hyperbolic polygons, (2014)

[8] B Farb, D Margalit, A primer on mapping class groups, Princeton Mathematical Series 49, Princeton Univ. Press (2012)

[9] S Kojima, Y Miyamoto, The smallest hyperbolic $3$–manifolds with totally geodesic boundary, J. Differential Geom. 34 (1991) 175

[10] D Mumford, A remark on Mahler's compactness theorem, Proc. Amer. Math. Soc. 28 (1971) 289

[11] B P Palka, An introduction to complex function theory, Springer (1991)

[12] J M Schlenker, Small deformations of polygons and polyhedra, Trans. Amer. Math. Soc. 359 (2007) 2155

[13] E Vanderzee, A N Hirani, D Guoy, E A Ramos, Well-centered triangulation, SIAM J. Sci. Comput. 31 (2009/10) 4497

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