F. Avram and D. Bertsimas, On central limit theorems in geometrical probability, The Annals of Applied Probability, pp.1033-1046, 1993.

C. B. Allendoerfer, The Euler number of a Riemann manifold, American Journal of Mathematics, vol.62, issue.1, pp.243-248, 1940.

E. Artin, The Gamma Function. Athena Series: Selected topics in mathematics. Holt, Rinehart and Winston, 1964.

F. Baccelli and B. B?aszczyszyn, On a coverage process ranging from the Boolean model to the Poisson-Voronoi tessellation with applications to wireless communications, Adv. in Appl. Probab, vol.33, issue.2, pp.293-323, 2001.
URL : https://hal.archives-ouvertes.fr/inria-00072622

F. Baccelli and B. B?aszczyszyn, Stochastic geometry and wireless networks: Volume II applications, Foundations and Trends R in Networking, vol.4, issue.1-2, pp.1-312, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00403040

A. Baddeley, I. Bárány, and R. Schneider, Stochastic Geometry: Lectures Given at the CIME Summer School, 2004.

E. Bertin and J. Chassery, 3-D Voronoi diagram: application to segmentation, Conference C: Image, Speech and Signal Analysis, Proceedings., 11th IAPR International Conference on, vol.III, pp.197-200, 1992.

J. K. Beem, Pseudo-Riemannian manifolds with totally geodesic bisectors, Proc. Amer. Math. Soc, vol.49, pp.212-215, 1975.

M. Berger, A panoramic view of Riemannian geometry, 2003.

N. Bleistein and R. A. Handelsman, Asymptotic expansions of integrals, 1986.

J. Bismut, The Atiyah-Singer theorems: a probabilistic approach. i. the index theorem, Journal of functional analysis, vol.57, issue.1, pp.56-99, 1984.

J. Bismut, Index theorem and the heat equation, Proceedings of the International Congress of Mathematicians, vol.1, 1986.

A. Baddeley and E. B. Jensen, Stereology for statisticians, 2004.

F. Baccelli, M. Klein, M. Lebourges, and S. Zuyev, Géométrie aléatoire et architecture de réseaux, Annals of Telecommunications, vol.51, issue.3, pp.158-179, 1996.

V. Baumstark and G. Last, Some distributional results for Poisson-Voronoi tessellations, Adv. in Appl. Probab, vol.39, issue.1, pp.16-40, 2007.

W. Blaschke, Integralgeometrie 1. Ermittlung der Dichten für linear Unterräume im En, Actualités Scientifiques et Industrielles, vol.252, 1935.

O. Bonnet, Mémoire sur la théorie général des surfaces, p.1848

B. N. Boots, Some observation on the structure of socio-economic cellular networks. The Canadian Geographer/Le Géographe canadien, vol.19, pp.107-120, 1975.

Y. Baryshnikov and J. E. Yukich, Gaussian limits for random measures in geometric probability, The Annals of Applied Probability, vol.15, issue.1A, pp.213-253, 2005.

Y. D. Burago and V. A. Zalgaller, Geometric inequalities, 1980.

A. K. Chakravarti and O. W. Archibold, Patterns of diurnal variation of growing season precipitation on the Canadian prairies: a harmonic analysis. The Canadian Geographer/Le Géographe canadien, vol.37, pp.16-28, 1993.

P. Calka, The distributions of the smallest disks containing the Poisson-Voronoi typical cell and the Crofton cell in the plane, Advances in Applied Probability, vol.34, issue.4, pp.702-717, 2002.

P. Calka, An explicit expression for the distribution of the number of sides of the typical Poisson-Voronoi cell, Advances in Applied Probability, vol.35, issue.4, pp.863-870, 2003.

J. Cheeger and D. G. Ebin, Comparison theorems in Riemannian geometry, vol.365, 2008.

S. Chern, A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds, Ann. of Math, vol.45, issue.2, pp.747-752, 1944.

S. Chern, On the curvatura integra in a Riemannian manifold, Annals of Mathematics, pp.674-684, 1945.

C. B. Croke and H. Karcher, Volumes of small balls on open manifolds: lower bounds and examples, Transactions of the American Mathematical Society, vol.309, issue.2, pp.753-762, 1988.

J. Chassery and M. Melkemi, Diagramme de Voronoi appliqué a la segmentation d'images et a la détection d' événements en imagerie multi-sources, Traitement du signal, vol.8, issue.3, pp.155-164, 1991.

H. S. Coxeter, Non-Euclidean geometry, MAA Spectrum. Mathematical Association of America, 1998.

S. N. Chiu, D. Stoyan, W. S. Kendall, and J. Mecke, Stochastic geometry and its applications, 2013.

S. N. Chiu, R. Van-de-weygaert, and D. Stoyan, The sectional Poisson Voronoi tessellation is not a Voronoi tessellation, Advances in Applied Probability, vol.28, issue.2, pp.356-376, 1996.

P. Calka and J. E. Yukich, Variance asymptotics for random polytopes in smooth convex bodies. Probability Theory and Related Fields, vol.158, pp.435-463, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00710266

M. P. Carmo, Differential geometry of curves and surfaces, 1976.

M. P. Carmo, Mathematics: Theory & Applications, 1992.

X. Descombes, Stochastic geometry for image analysis, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00793677

G. Dirichlet, Über die Reduktion der positiven quadratischen Formen mit drei unbestimmten ganzen Zahlen, Journal für die reine und angewandte Mathematik, vol.40, pp.209-227, 1850.

D. J. Daley and D. Vere-jones, An introduction to the theory of point processes: volume II: general theory and structure, 2007.

P. Engel and H. Syta, Voronoï's Impact on Modern Science, Number livr. 1 in Mathematics and its applications. Institute of Mathematics, 1998.

S. G. Foss and S. Zuyev, On a Voronoi aggregative process related to a bivariate Poisson process, Advances in Applied Probability, vol.28, issue.4, pp.965-981, 1996.

K. F. Gauss, General investigations of curved surfaces of 1827 and 1825, 1902.

S. Gallot, D. Hulin, and J. Lafontaine, Riemannian geometry, vol.3, 1990.
URL : https://hal.archives-ouvertes.fr/hal-00002870

F. Gao, D. Hug, and R. Schneider, Intrinsic volumes and polar sets in spherical space, Math. Inst, 2003.

E. N. Gilbert, Random subdivisions of space into crystals, The Annals of mathematical statistics, vol.33, issue.3, pp.958-972, 1962.

P. B. Gilkey, The boundary integrand in the formula for the signature and Euler characteristic of a Riemannian manifold with boundary, Advances in Mathematics, vol.15, issue.3, pp.334-360, 1975.

D. Gentner and G. Last, Palm pairs and the general mass-transport principle, Mathematische Zeitschrift, vol.267, issue.3-4, pp.695-716, 2011.

P. Gilkey and J. H. Park, Analytic continuation, the Chern-Gauss-Bonnet theorem, and the Euler-Lagrange equations in Lovelock theory for indefinite signature metrics, Journal of Geometry and Physics, vol.88, pp.88-93, 2015.

A. Gray, The volume of a small geodesic ball of a Riemannian manifold, Michigan Math. J, vol.20, pp.329-344, 1973.

M. Gromov, Curvature, diameter and Betti numbers, Commentarii Mathematici Helvetici, vol.56, issue.1, pp.179-195, 1981.

P. B. Gilkey and D. Toledo, Invariance theory, the heat equation, and the Atiyah-Singer index theorem, Publish or Perish Wilmington, vol.11, 1984.

M. Gerstein, J. Tsai, and M. Levitt, The volume of atoms on the protein surface: calculated from simulation, using Voronoi polyhedra, Journal of molecular biology, vol.249, issue.5, pp.955-966, 1995.

A. Hatcher, Algebraic Topology, 2002.

L. Heinrich and I. S. Molchanov, Central limit theorem for a class of random measures associated with germ-grain models, Advances in Applied Probability, vol.31, issue.2, pp.283-314, 1999.

H. Hopf, Über die Curvatura integra geschlossener Hyperflächen. Mathematische Annalen, vol.95, pp.340-367, 1926.

D. Hug and M. Reitzner, Gaussian polytopes: variances and limit theorems, Advances in applied probability, vol.37, issue.2, pp.297-320, 2005.

D. Hug and A. Reichenbacher, Geometric inequalities, stability results and Kendall's problem in spherical space, 2017.

D. Hug, M. Reitzner, and R. Schneider, Large Poisson-Voronoi cells and Crofton cells, Adv. in Appl. Probab, vol.36, issue.3, pp.667-690, 2004.

D. Hug, M. Reitzner, and R. Schneider, The limit shape of the zero cell in a stationary Poisson hyperplane tessellation, Annals of probability, pp.1140-1167, 2004.

D. Hug and R. Schneider, Large typical cells in Poisson-Delaunay mosaics, Revue Roumaine de Mathematiques Pures et Appliquees, vol.50, pp.657-670, 2005.

D. Hug and R. Schneider, Asymptotic shapes of large cells in random tessellations, GAFA Geometric And Functional Analysis, vol.17, issue.1, pp.156-191, 2007.

L. Heinrich, H. Schmidt, and V. Schmidt, Central limit theorems for Poisson hyperplane tessellations, The Annals of Applied Probability, vol.16, issue.2, pp.919-950, 2006.

. Ep and . Hsu, Stochastic local Gauss-Bonnet-Chern theorem, Journal of Theoretical Probability, vol.10, issue.4, pp.819-834, 1997.

Y. Isokawa, Poisson-Voronoi tessellations in three-dimensional hyperbolic spaces, Adv. in Appl. Probab, vol.32, issue.3, pp.648-662, 2000.

Y. Isokawa, Some mean characteristics of Poisson-Voronoi and Poisson-Delaunay tessellations in hyperbolic planes, Bull. Fac. Ed. Kagoshima Univ. Natur. Sci, vol.52, pp.11-25, 2000.

S. R. Jammalamadaka and S. Janson, Limit theorems for a triangular scheme of u-statistics with applications to inter-point distances, The Annals of Probability, vol.14, issue.4, pp.1347-1358, 1986.

D. L. Johnson and F. Morgan, Some sharp isoperimetric theorems for Riemannian manifolds, Indiana University Mathematics Journal, pp.1017-1041, 2000.

W. S. Kendall, G. Last, and I. S. Molchanov, New perspectives in stochastic geometry, Oberwolfach Reports, vol.5, issue.4, pp.2655-2702, 2009.

I. N. Kovalenko, A proof of a conjecture of David Kendall on the shape of random polygons of large area, Kibernet. Sistem. Anal, vol.4, pp.3-10, 1997.

J. M. Lee, Riemannian manifolds, Graduate Texts in Mathematics, vol.176, 1997.

S. Lee, The central limit theorem for Euclidean minimal spanning trees i, The Annals of Applied Probability, vol.7, issue.4, pp.996-1020, 1997.

S. Lee, The central limit theorem for Euclidean minimal spanning trees ii, Advances in Applied Probability, vol.31, issue.4, pp.969-984, 1999.

J. M. Lee, Smooth manifolds, Introduction to Smooth Manifolds, pp.1-29, 2003.

J. M. Lee, Riemannian manifolds: an introduction to curvature, vol.176, 2006.

G. Leibon, Random Delaunay triangulations, the Thurston-Andreev theorem, and metric uniformization, ProQuest LLC, 1999.

G. Leibon, Random Delaunay triangulations and metric uniformization, Int. Math. Res. Not, vol.25, pp.1331-1345, 2002.

F. Lips, Moyennes empiriques pour les mosaïques de Voronoi du disque de Poincaré, Comptes Rendus Mathematique, vol.342, issue.10, pp.767-772, 2006.

G. Leibon and D. Letscher, Delaunay triangulations and Voronoi diagrams for Riemannian manifolds, Proceedings of the sixteenth annual symposium on Computational geometry, pp.341-349, 2000.

G. Last and M. Penrose, Lectures on the Poisson process, vol.7, 2017.

G. Last, G. Peccati, and M. Schulte, Normal approximation on Poisson spaces: Mehler's formula, second order poincaré inequalities and stabilization. Probability theory and related fields, vol.165, pp.667-723, 2016.

G. Last, M. D. Penrose, M. Schulte, and C. Thäle, Moments and central limit theorems for some multivariate poisson functionals, Advances in Applied Probability, vol.46, issue.2, pp.348-364, 2014.

R. Lachièze-rey and G. Peccati, Fine gaussian fluctuations on the poisson space, i: contractions, cumulants and geometric random graphs, Electronic Journal of Probability, vol.18, 2013.

J. L. Meijering, Interface area, edge length, and number of vertices in crystal aggregates with random nucleation, Philips Res. Rep, vol.8, pp.270-290, 1953.

R. E. Miles, Poisson flats in Euclidean spaces, Izv. Akad. Nauk Armjan. SSR Ser. Mat, vol.5, issue.3, pp.263-285, 1970.

R. E. Miles, Isotropic random simplices, Adv. in Appl. Probab, vol.3, pp.353-382, 1971.

R. E. Miles, Random points, sets and tessellations on the surface of a sphere, Sankhy? Ser. A, vol.33, pp.145-174, 1971.

R. E. Miles, Sectional Voronoi tessellations, Rev. Un. Mat. Argentina, vol.29, pp.310-327, 1984.

R. E. Miles, A heuristic proof of a long-standing conjecture of D.G. Kendall concerning the shapes of certain large random polygons, Advances in applied probability, vol.27, issue.2, pp.397-417, 1995.

J. Møller, Random tessellations in R d, Adv. in Appl. Probab, vol.21, issue.1, pp.37-73, 1989.

J. Møller, Lectures on random Vorono? tessellations, Lecture Notes in Statistics, vol.87, 1994.

V. Mathai and D. Quillen, Superconnections, Thom classes, and equivariant differential forms, Topology, vol.25, issue.1, pp.85-110, 1986.

V. D. Milman and G. Schechtman, Asymptotic theory of finite dimensional normed spaces: Isoperimetric inequalities in Riemannian manifolds, vol.1200, 1986.

V. J. Martinez and E. Saar, Statistics of the galaxy distribution, 2001.

R. E. Miles and J. Serra, Microscale modelling of fruit tissue using Voronoi tessellations. Computers and electronics in agriculture, Geometrical Probability and Biological Structures: Buffon's 200th Anniversary: Proceedings of the Buffon Bicentenary Symposium on Geometrical Probability, Image Analysis, vol.23, pp.36-48, 1977.

I. S. Molchanov and S. Zuyev, Variational analysis of functionals of Poisson processes, Mathematics of Operations Research, vol.25, issue.3, pp.485-508, 2000.

J. Ohser and F. Mücklich, Statistical analysis of microstructures in materials science, 2000.

M. D. Penrose, Laws of large numbers in stochastic geometry with statistical applications, Bernoulli, vol.13, issue.4, pp.1124-1150, 2007.

B. Petkantschin, Integralgeometrie 6. Zusammenhänge zwischen den Dichten der linearen Unterräume im n-dimensionalen Raum, Abh. Math. Sem. Univ. Hamburg, vol.11, issue.1, pp.249-310, 1935.

M. D. Penrose and J. E. Yukich, Central limit theorems for some graphs in computational geometry, Annals of Applied probability, pp.1005-1041, 2001.

M. D. Penrose and J. E. Yukich, Weak laws of large numbers in geometric probability, Annals of Applied probability, pp.277-303, 2003.

M. D. Penrose and J. E. Yukich, Limit theory for point processes in manifolds, The Annals of Applied Probability, vol.23, issue.6, pp.2161-2211, 2013.

M. Reitzner and M. Schulte, Central limit theorems for u-statistics of Poisson point processes. The Annals of Probability, vol.41, pp.3879-3909, 2013.

R. Schneider, Weighted faces of Poisson hyperplane tessellations, Adv. in Appl. Probab, vol.41, issue.3, pp.682-694, 2009.

R. Schneider, Convex bodies: the Brunn-Minkowski theory. Number 151. Cambridge university press, 2014.

D. Stoyan, J. Mecke, and W. Kendall, Stochastic geometry and its applications, 1995.

I. Shigekawa, N. Ueki, and S. Watanabe, A probabilistic proof of the Gauss-Bonnet-Chern theorem for manifolds with boundary, 1989.

R. Schneider and W. Weil, Stochastic and integral geometry, 2008.

T. Tao, Ricci flow, 2008.

J. A. Thorpe, Elementary topics in differential geometry, 2012.

R. Van-de-weygaert, Fragmenting the universe. 3: The constructions and statistics of 3-D Voronoi tessellations, Astronomy and Astrophysics, vol.283, pp.361-406, 1994.

R. Van-de-weygaert, Fragmenting the universe III: The construction and statistics of 3-D Voronoi tessellations, Astronomy and astrophysics (Berlin. Print), vol.283, issue.2, pp.361-406, 1994.

E. B. Jensen and K. Kiêu, A new integral geometric formula of the BlaschkePetkantschin type, Mathematische Nachrichten, vol.156, issue.1, pp.57-74, 1992.

G. Voronoï, Nouvelles applications des paramètres continus à la théorie des formes quadratiques. deuxième mémoire. recherches sur les parallélloèdres primitifs, Journal für die reine und angewandte Mathematik, vol.134, pp.198-287, 1908.

S. Yau, Some function-theoretic properties of complete Riemannian manifold and their applications to geometry, Indiana University Mathematics Journal, vol.25, issue.7, pp.659-670, 1976.

H. Zessin, Point processes in general position, Journal of Contemporary Mathematical Analysis, vol.43, issue.1, pp.59-65, 2008.

S. Zuyev, Strong Markov property of Poisson processes and Slivnyak formula, Case studies in spatial point process modeling, pp.77-84, 2006.