## Stability theorems for mappings with bounded excursions.(English)Zbl 0176.03503

### Keywords:

complex functions
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### References:

 [1] Yu. G. Reshetnyak, Bounds on the Modulus of Continuity for Certain Mappings, Sibirsk. Matem. Zh.,2, No.5, 1106-1114 (1966). [2] Yu. G. Reshetnyak, Spatial Mappings with Bounded Excursions, Sibirsk. Matem. Zh.,8, No.3, 629-658 (1967). [3] Yu. G. Reshetnyak, Liouville’s Theorem with Minimal Assumptions as to Regularity, Sibirsk. Matem. Zh.,8, No.4, 835-840 (1967). [4] Yu. G. Reshetnyak, On Stability of Conformal Mappings in Multidimensional Spaces, Sibirsk. Matem. Zh.,8, No.1, 111-134 (1967). [5] Yu. G. Reshetnyak, On Stability in Liouville’s Theorem on Conformal Mappings of Spaces, Dokl. Akad. Nauk SSSR,152, No.2, 286-287 (1963). [6] S. L. Sobolev, Certain Applications of Functional Analysis to Mathematical Physics [in Russian], Izdvo Len. Gos. In-ta, Leningrad (1950). · Zbl 0041.52307 [7] Yu. G. Reshetnyak, Certain Geometric Properties of Functions and Mappings with Generalized Derivatives, Sibirsk. Matem. Zh.,7, No.4, 886-919 (1966). [8] G. de Rham, Differentiable Varieties [Russian translation], IL, Moscow (1956). [9] Yu. E. Borovskii, Completely Integrable Pfaff Systems, Izv. Vyssh. Uch. Zav., Matem.,2, No.2, 28-40 (1959). [10] I. M. Gel’fand and G. E. Shilov, Generalized Functions and Actions on Them [in Russian], Fizmatgiz, Moscow (1959). · Zbl 0091.11102 [11] A. D. Aleksandrov, Additive Set Functions in Abstract Spaces [in English], Matem. Sb.,9, 563-628 (1941). · Zbl 0028.07201 [12] Yu. G. Reshetnyak, Mappings with Bounded Excursions as Extremals of Dirichlet-Type Integrals, Sibirsk. Matem. Zh.,9, No.3, 652-666 (1968). [13] Yu. G. Reshetnyak, General Theorems on Semicontinuity and on Convergence with Functionals, Sibirsk. Matem. Zh.,8, No.5, 1051-1069 (1967). [14] P. P. Belinskii, On Continuity of Spatial Quasiconformal Mappings and on Liouville’s Theorem, Dokl. Akad. Nauk SSSR,147, No.5, 1003-1004 (1962).
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