Energy spectrum of certain harmonic mappings
Adachi, Toshiaki ; Sunada, Toshikazu
Compositio Mathematica, Tome 56 (1985), p. 153-170 / Harvested from Numdam
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Publié le : 1985-01-01
@article{CM_1985__56_2_153_0,
     author = {Adachi, Toshiaki and Sunada, Toshikazu},
     title = {Energy spectrum of certain harmonic mappings},
     journal = {Compositio Mathematica},
     volume = {56},
     year = {1985},
     pages = {153-170},
     mrnumber = {809864},
     zbl = {0578.58009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1985__56_2_153_0}
}

Adachi, Toshiaki; Sunada, Toshikazu. Energy spectrum of certain harmonic mappings. Compositio Mathematica, Tome 56 (1985) pp. 153-170. http://gdmltest.u-ga.fr/item/CM_1985__56_2_153_0/

[1] R.L. Bishop and R.J. Crittenden: Geometry of Manifold, Academic Press: New York and London (1964). | MR 169148 | Zbl 0132.16003

[2] P. Buser and H. Karcher: Gromov's almost flat manifolds, Asterisque 81 (1981). | MR 619537 | Zbl 0459.53031

[3] J. Eells and J. Sampson: Harmonic mappings of Riemannian manifold, Amer. J. Math. 86 (1964) 109-160. | MR 164306 | Zbl 0122.40102

[4] J. Eells and L. Lemaire: A report on harmonic maps, Bull. London Math. Soc. 10 (1978) 1-68. | MR 495450 | Zbl 0401.58003

[5] S. Gallot: Inégalité isoperimetrique sur les variétés compactes sans bord, to appear.

[6] R. Gangolli: On the length spectra of certain compact manifolds of negative curvature J. Diff. Geom. 12 (1977) 403-424. | MR 650997 | Zbl 0365.53016

[7] M. Gromov: Structures metriques sur les variétés riemannienes (rédigé par J. Lafontaine et P. Pansu), Cedic, Paris (1982). | MR 682063 | Zbl 0509.53034

[8] P. Hartman: On homotopic harmonic maps, Can. J. Math. 19 (1967) 673-687. | MR 214004 | Zbl 0148.42404

[9] N. Hingston: Equivariant Morse theory and closed geodesics, preprint. | MR 739783 | Zbl 0561.58007

[10] H. Huber: Über die Isometriegruppe einer kompakten Mannigfaltigkeit mit negativer Krümmung, Helv. Phys. Acta 45 (1972) 277-288.

[11] H.C. Im Hof: Über die Isometriegruppe bei kompakten Mannigfaltigkeiten negativer Krümmung, Comment. Math. Helv. 48 (1973) 14-30. | MR 328819 | Zbl 0258.53040

[12] M. Kalka, B. Shiffman and B. Wong: Finiteness and rigidities theorem for holomorphic mappings, Michigan Math. J. 28 (1981) 289-295. | MR 629361 | Zbl 0459.32011

[13] S. Kobayashi and K. Nomizu: Foundations of Differential Geometry, John Wiley & Sons: New Nork (1963). | Zbl 0119.37502

[14] L. Lemaire: Harmonic mappings of uniform bounded dilatation, Topology 16 (1977) 199-201. | MR 448412 | Zbl 0343.53029

[15] P. Li: On the Sobolev constant and the p-spectrum of a compact Riemannian manifolds, Ann. scient. Éc. Norm. Sup. 13 (1980) 451-469. | Numdam | MR 608289 | Zbl 0466.53023

[16] N. Maeda: The isometry groups of compact manifolds with non-positive curvature, Proc. Japan Acad. 51 (1975) 790-794. | MR 397616 | Zbl 0341.53026

[17] A. Manning: Topological entropy for geodesic flows, Ann. of Math. 110 (1979) 567-573. | MR 554385 | Zbl 0426.58016

[18] G.A. Margulis: Applications of ergodic theory to the investigation of manifolds of negative curvature, Funct. Analy. and Appl. 3 (1969) 335-336. | MR 257933 | Zbl 0207.20305

[19] T. Nagano and B. Smyth: Minimal varieties and harmonic maps in tori, Comment. Math. Helu. 50 (1975) 249-265. | MR 390974 | Zbl 0326.53055

[20] J. Noguchi and T. Sunada: Finiteness of the family of rational and meromorphic mappings into algebraic varieties, Amer. J. Math. 104 (1982) 887-900. | MR 667540 | Zbl 0502.14002

[21] H.L. Royden: The Ahlfors-Schwarz lemma in several complex variables, Comment. Math. Helv. 55 (1980) 547-558. | MR 604712 | Zbl 0484.53053

[22] R. Schoen and S.T. Yau: Compact group actions and the topology of manifolds with non-positive curvature, Topology 18 (1979) 361-380. | MR 551017 | Zbl 0424.58012

[23] T. Sunada: Holomorphic mappings into a compact quotient of symmetric bounded domain, Nagoya Math. J. 64 (1976) 159-175. | MR 419848 | Zbl 0352.32030

[24] T. Sunada: Rigidity of certain harmonic mappings, Invent. Math. 51 (1979) 297-307. | MR 530636 | Zbl 0418.31005

[25] T. Sunada: Tchebotarev's density theorem for closed geodesics in a compact locally symmetric space of negative curvature, preprint.

[26] T. Sunada: Geodesic flows and geodesic random walks, to appear in Advanced Studies in Pure Math. 3. | MR 758647 | Zbl 0599.58037

[27] K. Uhlenbeck: Morse theory by perturbation methods with applications to harmonic maps, Trans. AMS. 267 (1981) 569-583. | MR 626490 | Zbl 0509.58012

[28] A. Howard and A.J. Sommese, On the orders of the automorphism groups of certain projective manifolds, Progress in Math. 14 (1981) 145-158. | MR 642855 | Zbl 0483.32016

[29] W. Parry and M. Pollicott: An analogue of the prime number theorem for closed orbits of Axion A flows, preprint. | MR 727704 | Zbl 0537.58038

[30] J. Vilms: Totally geodesic maps, J. Differential Geom. 4 (1970) 73-79. | MR 262984 | Zbl 0194.52901