Liouville coverings of complex spaces, and amenable groups
Sbornik. Mathematics, Tome 60 (1988) no. 1, pp. 197-216 Cet article a éte moissonné depuis la source Math-Net.Ru

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The author determines conditions under which a connected unramified holomorphic covering of a Liouville space is again a Liouville space. Bibliography: 31 titles.
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     title = {Liouville coverings of complex spaces, and amenable groups},
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V. Ya. Lin. Liouville coverings of complex spaces, and amenable groups. Sbornik. Mathematics, Tome 60 (1988) no. 1, pp. 197-216. http://geodesic.mathdoc.fr/item/SM_1988_60_1_a11/

[1] Nori A., “A note on unramified abelian covering surfaces of closed Riemann surface”, J. Math. Soc. Japan, 6:2 (1954), 162–176 | MR

[2] Shabat G. B., “Liuvillevost maksimalnykh abelevykh pokrytii rimanovykh poverkhnostei”, UMN, 39:2 (1984), 131–132 | MR | Zbl

[3] Wakabayashi I., “Nonexistence of bounded functions on the homology covering surface of $\mathbf{P}^1/\{$3 points$\}$”, J. Math. Soc. Japan, 34:4 (1982), 607–625 | DOI | MR | Zbl

[4] Demailli J.-P., “Fonctions holomorphes à croissance polynomiale sur la surface d'équation $e^x+e^y=1$”, Bull. Sci. Math. Paris. Ser. 2, 303:2 (1979), 179–191

[5] Borel A., Narasimhan R., “Uniqueness conditions for certain holomorphic mappings”, Invent. Math., 2 (1967), 247–255 | DOI | MR | Zbl

[6] Lyons T., Sullivan D., “Function theory, random paths and covering spaces”, J. Diff. Geom., 19:2 (1984), 299–323 | MR | Zbl

[7] Veil A., Vvedenie v teoriyu kelerovykh mnogoobrazii, IL, M., 1961

[8] Kaimanovich V. A., “Brounovskoe dvizhenie i gramonicheskie funktsii na nakryvayuschikh mnogoobraziyakh – entropiinyi podkhod”, DAN SSSR, 288:5 (1986), 1045–1049 | MR | Zbl

[9] Vershik A. M., Kaimanovich V. A., “Sluchainye bluzhdaniya na gruppakh: granitsa, entropiya, ravnomernoe raspredelenie”, DAN SSSR, 249:1 (1979), 15–18 | MR | Zbl

[10] Vershik A. M., Kaimanovich V. A., “Random walks on discrete groups: boundary and entropy”, Ann. of Probability, 11:3 (1983), 457–490 | DOI | MR | Zbl

[11] Avez A., “Theoreme de Choquet–Deny pour les groupes à croissance non exponentionelle”, C. R. Acad. Sci. Paris, 279A (1974), 25–28 | MR

[12] Zaidenberg M. G., Lin V. Ya., “Teoremy konechnosti dlya golomorfnykh otobrazhenii”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 9, VINITI, M., 1986, 127–193 | MR

[13] Grinlif F., Invariantnye srednie na topologicheskikh gruppakh i ikh primeneniya, Mir, M., 1973

[14] Cartan H., “Quotent d'un espace analytique par un groupe d'automorphismes”, Algebraic geometry and algebraic topology. A Symposium in honour of S. Lefscheth, Princeton Univ. Press, Princeton, 1957, 90–102 | MR | Zbl

[15] Vladimirov V. S., Metody teorii funktsii mnogikh kompleksnykh peremennykh, Nauka, M., 1964 | MR

[16] Brelo M., O topologiyakh i granitsakh v teorii potentsiala, Mir, M., 1974 | MR | Zbl

[17] Maeda F.-J., “Dirichlet integrals on harmonic spaces”, Lecture Notes Math., 803, Springer-Verlag, Berlin, 1980 | MR | Zbl

[18] Hervé R.-M., “Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel”, Ann. Inst. Fourier, 12 (1962), 415–571 | MR | Zbl

[19] Constantinescu C., Cornea A., Potential theory on harmonic spaces, Springer-Verlag, Berlin, 1972 | MR | Zbl

[20] Miranda K., Uravneniya s chastnymi proizvodnymi ellipticheskogo tipa, IL, M., 1957

[21] Kurosh A. G., Teoriya grupp, Nauka, M., 1967 | MR | Zbl

[22] Dynkin E. B., Malyutov M. B., “Sluchainoe bluzhdanie na gruppakh s konechnym chislom obrazuyuschikh”, DAN SSSR, 137:5 (1961), 1042–1045 | MR | Zbl

[23] Margulis G. A., “Polozhitelnye garmonicheskie funktsii na nilpotentnykh gruppakh”, DAN SSSR, 166:5 (1966), 1054–1057 | MR | Zbl

[24] Pyatetskii-Shapiro I. I., “Avtomorfnye funktsii i arifmeticheskie gruppy”, Tr. mezhdunarodnogo kongressa matematikov (Moskva–1966), Mir, M., 1968, 232–247

[25] Shabat G. B., “O kompleksnoi strukture oblastei, nakryvayuschikh algebraicheskie poverkhnosti”, Funktsion. analiz i ego pril., 11:2 (1977), 67–75 | MR | Zbl

[26] Ohsawa T., “A remark on the completeness of the Bergman metric”, Proc. Japan Acad. Ser. A, 57:4 (1981), 238–240 | DOI | MR | Zbl

[27] Inoue M., “On surfaces of class VII”, Invent. math., 24:4 (1974), 269–310 | DOI | MR | Zbl

[28] Fam F., Osobennosti protsessov mnogokratnogo rasseyaniya, Mir, M., 1972 | MR

[29] Yau S.-T., “Harmonic functions on complete Riemannian manifolds”, Comm. Pure Appl. Math., 28:2 (1975), 201–228 | DOI | MR | Zbl

[30] Cheng S. Y., Yau S. T., “Differential equations on Riemannian manifolds and their geometric applications”, Comm. Pure Appl. Math., 28:3 (1975), 333–354 | DOI | MR | Zbl

[31] Grigoryan A. A., “O suschestvovanii polozhitelnykh fundamentalnykh reshenii uravneniya Laplasa na rimanovykh mnogoobraziyakh”, Matem. sb., 128(170):3 (1985), 354–363 | MR