Conformal immersions of complete Riemannian manifolds and extensions of the Schwarz Lemma
Andrea Ratto, Marco Rigoli, and Laurent Veron
Source: Duke Math. J. Volume 74, Number 1
(1994), 223-236.
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077288017
Mathematical Reviews number (MathSciNet): MR1271471
Zentralblatt MATH identifier: 0813.53038
Digital Object Identifier: doi:10.1215/S0012-7094-94-07411-5
References
[1] K. Akutagawa and A. Tachikawa, Nonexistence results for harmonic maps between noncompact, complete Riemannian manifolds, to appear in Tokyo J. Math.
Mathematical Reviews (MathSciNet): MR1223292
Zentralblatt MATH: 0791.53044
[2] E. Calabi, An extension of E. Hopf's maximum principle with an application to Riemannian geometry, Duke Math. J. 25 (1957), 45–56.
Mathematical Reviews (MathSciNet): MR19,1056e
Zentralblatt MATH: 0079.11801
Digital Object Identifier: doi:10.1215/S0012-7094-58-02505-5
Project Euclid: euclid.dmj/1077467776
[3] S. Y. Cheng, Liouville theorem for harmonic maps, Geometry of the Laplace operator (Proc. Sympos. Pure Math., Univ. Hawaii, Honolulu, Hawaii, 1979), Proc. Sympos. Pure Math., XXXVI, Amer. Math. Soc., Providence, R.I., 1980, pp. 147–151.
Mathematical Reviews (MathSciNet): MR81i:58021
Zentralblatt MATH: 0455.58009
[4] K.-S. Cheng and J.-T. Lin, On the elliptic equations $\Delta u=K(x)u\sp \sigma$ and $\Delta u=K(x)e\sp 2u$, Trans. Amer. Math. Soc. 304 (1987), no. 2, 639–668.
Mathematical Reviews (MathSciNet): MR88j:35054
Zentralblatt MATH: 0635.35027
Digital Object Identifier: doi:10.2307/2000734
JSTOR: links.jstor.org
[5] J. Eells and L. Lemaire, Another report on harmonic maps, Bull. London Math. Soc. 20 (1988), no. 5, 385–524.
Mathematical Reviews (MathSciNet): MR89i:58027
Zentralblatt MATH: 0669.58009
Digital Object Identifier: doi:10.1112/blms/20.5.385
[6] J. Eells and L. Lemaire, Selected topics in harmonic maps, CBMS Regional Conference Series in Mathematics, vol. 50, Published for the Conference Board of the Mathematical Sciences, Washington, DC, 1983.
Mathematical Reviews (MathSciNet): MR85g:58030
Zentralblatt MATH: 0515.58011
[7] R. E. Greene and H.-H. Wu, Function theory on manifolds which possess a pole, Lecture Notes in Mathematics, vol. 699, Springer, Berlin, 1979.
Mathematical Reviews (MathSciNet): MR81a:53002
Zentralblatt MATH: 0414.53043
[8] D. Hulin, Déformation conforme des surfaces non compactes à courbure négative, J. Funct. Anal. 111 (1993), no. 2, 449–472.
Mathematical Reviews (MathSciNet): MR94g:53034
Zentralblatt MATH: 0788.53032
Digital Object Identifier: doi:10.1006/jfan.1993.1021
[9] J. L. Kazdan, Prescribing the curvature of a Riemannian manifold, CBMS Regional Conference Series in Mathematics, vol. 57, Published for the Conference Board of the Mathematical Sciences, Washington, DC, 1985.
Mathematical Reviews (MathSciNet): MR86h:53001
Zentralblatt MATH: 0561.53048
[10] A. Lichnerowicz, Géométrie des groupes de transformations, Travaux et Recherches Mathématiques, III. Dunod, Paris, 1958.
Mathematical Reviews (MathSciNet): MR23:A1329
Zentralblatt MATH: 0096.16001
[11] M. Obata, Conformal transformations of compact Riemannian manifolds, Illinois J. Math. 6 (1962), 292–295.
Mathematical Reviews (MathSciNet): MR25:1507
Zentralblatt MATH: 0107.15703
Project Euclid: euclid.ijm/1255632326
[12] H. L. Royden, The Ahlfors-Schwarz lemma in several complex variables, Comment. Math. Helv. 55 (1980), no. 4, 547–558.
Mathematical Reviews (MathSciNet): MR82i:32049
Zentralblatt MATH: 0484.53053
Digital Object Identifier: doi:10.1007/BF02566705
[13] M. Troyanov, The Schwarz lemma for nonpositively curved Riemannian surfaces, Manuscripta Math. 72 (1991), no. 3, 251–256.
Mathematical Reviews (MathSciNet): MR92f:53043
Zentralblatt MATH: 0736.53043
Digital Object Identifier: doi:10.1007/BF02568278
[14] K. Yano and T. Nagano, Einstein spaces admitting a one-parameter group of conformal transformations, Ann. of Math. (2) 69 (1959), 451–461.
Mathematical Reviews (MathSciNet): MR21:345
Zentralblatt MATH: 0088.14204
Digital Object Identifier: doi:10.2307/1970193
JSTOR: links.jstor.org
[15] S.-T. Yau, Remarks on conformal transformations, J. Differential Geometry 8 (1973), 369–381.
Mathematical Reviews (MathSciNet): MR49:3770
Zentralblatt MATH: 0274.53047
Project Euclid: euclid.jdg/1214431798
[16] S. T. Yau, A general Schwarz lemma for Kähler manifolds, Amer. J. Math. 100 (1978), no. 1, 197–203.
Mathematical Reviews (MathSciNet): MR58:6370
Zentralblatt MATH: 0424.53040
Digital Object Identifier: doi:10.2307/2373880
JSTOR: links.jstor.org
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