Geodesic
Quasiconformal Immersions of Riemannian Manifolds and a Picard Type Theorem
Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 3, pp. 37-48.

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We study singularities of quasiconformal immersions of Riemannian manifolds and show that the phenomenon of compulsory continuation holds in dimension $n\ge3$. In particular, this result in a stronger version of the Picard theorem—one without omitted values. 
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V. A. Zorich. Quasiconformal Immersions of Riemannian Manifolds and a Picard Type Theorem. Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 3, pp. 37-48. http://geodesic.mathdoc.fr/item/FAA_2000_34_3_a3/

[1] Ahlfors L., Beurling A., “Conformal invariants and function-theoretic null-sets”, Acta Math., 83 (1950), 101–129 | DOI | MR | Zbl

[2] Fuglede B., “Extremal length and functional completion”, Acta Math., 98 (1957), 171–219 | DOI | MR | Zbl

[3] Gehring F. W., “Extremal length definitions for the conformal capacity of rings in space”, Michigan Math. J., 9 (1962), 137–150 | DOI | MR | Zbl

[4] Aikawa H., Ohtsuka M., “Extremal length of vector measures”, Ann. Acad. Sci. Fenn. Math., 24:1 (1999), 61–89 | MR

[5] Zorich V. A., Keselman V. M., “O konformnom tipe rimanova mnogoobraziya”, Funkts. analiz i ego pril., 30:2 (1996), 40–55 | DOI | MR | Zbl

[6] Zorich V. A., “Asymptotic geometry and conformal types of Carnot–Carathéodory spaces”, Geom. Funct. Anal., 9:2 (1999), 393–411 | DOI | MR | Zbl

[7] Zorich V. A., “Teorema M. A. Lavrenteva o kvazikonformnykh otobrazheniyakh prostranstva”, Matem. sb., 74 (1967), 417–433 | Zbl

[8] Lavrentev M. A., “Ob odnom differentsialnom priznake gomeomorfnykh otobrazhenii trekhmernykh oblastei”, DAN SSSR, 20 (1938), 241–242 | MR

[9] Zorich V. A., “The global homeomorphism theorem for space quasiconformal mappings, its development and related open problems”, Lecture Notes in Math., 1508, Springer-Verlag, Berlin, 1992, 131–148 | MR

[10] Gromov M., “Hyperbolic manifolds, groups and actions”, Proceedings of the 1978 Stony Brook Conference, Ann. Math. Stud., 97, Princeton Univ. Press, Princeton, NJ, 1981, 183–213 | MR

[11] Gromov M., Metric structures for Riemannian and non-Riemannian spaces, Birkhäuser, Boston–Basel–Berlin, 1999, with appendices by Katz M., Pansu P., and Semmes S. | MR | Zbl