Philippe, Emmanuel On the rigidity of triangle groups \((r,p,q)\). (Sur la rigidité des groupes de triangles \((r,p,q)\).) (French) Zbl 1248.20053 Geom. Dedicata 149, 155-160 (2010). Summary: We show the length spectral rigidity for the family of Fuchsian triangular groups. Cited in 2 Documents MSC: 20H10 Fuchsian groups and their generalizations (group-theoretic aspects) 30F60 Teichmüller theory for Riemann surfaces 53C22 Geodesics in global differential geometry 20F05 Generators, relations, and presentations of groups 20F65 Geometric group theory Keywords:Fuchsian triangle groups; moduli of Riemann surfaces; geodesics; length spectra; hyperbolic surfaces PDFBibTeX XMLCite \textit{E. Philippe}, Geom. Dedicata 149, 155--160 (2010; Zbl 1248.20053) Full Text: DOI References: [1] Beardon A.F.: The Geometry of Discrete Groups, Graduate Texts in Mathematics. Springer, Berlin (1983) [2] Buser, P.: Geometry and spectra of compact riemann surfaces. Prog. Math. 106, Birkhäuser (1992) · Zbl 0770.53001 [3] Buser, P., Semmler, K.-D.: The geometry and spectrum of the one holed torus. Comment. Math. Helv. 63, 259–274 (1988) · Zbl 0649.53028 · doi:10.1007/BF02566766 [4] Dianu, R.: Sur le spectre des tores pointés. Thèse, EPFL, Lausanne (2000) [5] Dryden, E., Strohmaïer, A.: Huber’s theorem for hyperbolic orbisurfaces. Canadian Math. Bull. (to appear) · Zbl 1179.58014 [6] Dryden, E.: Geometric and spectral properties of compact Riemann orbisurfaces. Ph.D. Thesis, Dartmouth College (2004) [7] Haas A.: Length spectra as moduli for hyperbolics surfaces. Duke Math. J. 52, 922–935 (1985) · Zbl 0595.30052 · doi:10.1215/S0012-7094-85-05249-4 [8] Kac, M.: Can one hear the shape of a drum? The american mathematical monthly, 73(4), Part 2, Pap. Anal., pp. 1–23 (April 1966) · Zbl 0139.05603 [9] Katok S.: Fuchsian groups, Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL (1992) · Zbl 0753.30001 [10] Lehman, R., White, C.: Hyperbolic billiards path. http://www.tilings.org/pubs/TRlehmanwhite.pdf [11] Meyerhoff R.: A lower bound for the volume of hyperbolic 3-manifolds. Can. J. Math. 39(5), 1038–1056 (1987) · Zbl 0694.57005 · doi:10.4153/CJM-1987-053-6 [12] Philippe, E.: Géométrie des surfaces hyperboliques. Thèse, Université Paul Sabatier, Toulouse (2008) [13] Philippe, E.: Les groupes de triangles (2, p, q) sont déterminés par leur spectre des longueurs. Ann. Inst. Fourier 58(7), 2659–2693 (2008). http://arxiv.org/abs/0807.4746 [14] Philippe, E.: Sur le spectre des longueurs des groupes de triangles (r, p, q). http://arxiv.org/abs/0901.4630 [15] Ratcliffe J.G.: Foundations of Hyperbolic Manifolds, Graduate Texts in Mathematics. Springer, Berlin (1994) · Zbl 0809.51001 [16] Wolpert S.A.: The length spectra as moduli for compact Riemann surfaces. Ann. Math. 109, 323–351 (1979) · Zbl 0441.30055 · doi:10.2307/1971114 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.