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Stability of isometric mappings. (English. Russian original) Zbl 0546.30019

Sib. Math. J. 25, 274-283 (1984); translation from Sib. Mat. Zh. 25, No. 2(144), 132-144 (1984).
As application of the theory worked out by the author in ibid. 23, No.2, 83-111 (1982; Zbl 0509.32012), ibid. 23, No.4, 65-89 (1982; Zbl 0509.32013) and ibid. 24, No.5(141), 76-93 (1983; Zbl 0528.30011) in the present article the stability of quasi-isometric mappings introduced by F. John [Commun. Pure Appl. Math. 21, 77-110 (1968; Zbl 0157.458)] is investigated.

MSC:

30C62 Quasiconformal mappings in the complex plane
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References:

[1] A. P. Kopylov, ?Behavior of hyperplanes of quasiconformal maps of a space, close to conformal,? Dokl. Akad. Nauk SSSR,209, No. 6 (1973). · Zbl 0289.30029
[2] A. P. Kopylov, ?Boundary values of maps of a half-space, close to conformal,? Sib. Mat. Zh.,24, No. 5, 76-93 (1983). · Zbl 0528.30011
[3] A. P. Kopylov, ?Stability of classes of multidimensional holomorphic maps. I. Concept of stability. Liouville’s theorem,? Sib. Mat. Zh.,23, No. 2, 83-111 (1982). · Zbl 0509.32012
[4] A. P. Kopylov, ?Stability of classes of multidimensional holomorphic maps. II. Stability of classes of holomorphic maps,? Sib. Mat. Zh.,23, No. 4, 65-89 (1982). · Zbl 0585.76150
[5] A. P. Kopylov, ?Stability of classes of multidimensional holomorphic maps. III. Properties of maps close to conformal,? Sib. Mat. Zh.,24, No. 3, 70-91 (1983).
[6] F. John, ?Rotation and strain,? Commun. Pure Appl. Math.,14, No. 3, 391-413 (1961). · Zbl 0102.17404
[7] F. John, ?On quasiisometric mappings. I,? Commun. Pure Appl. Math.,21, No. 1, 77-110 (1968). · Zbl 0157.45803
[8] I. N. Vekua, Generalized Analytic Functions, Pergamon (1972). · Zbl 0092.29703
[9] F. John, ?On quasiisometric mappings. II,? Commun. Pure Appl. Math.,22, No. 2 (1969).
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