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Stability in the Cauchy and Morera Theorems for Holomorphic Functions and Their Spatial Analogs

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Abstract

Criteria are given for a mapping to have bounded distortion in terms of an integral estimate of the multiplicity function without any a priori assumption on the differential properties of the mapping. The result is most lucid and final in a sense for complex functions f:Δ⊂C→C of one complex variable. Generalizations to multidimensional Beltrami systems are suggested.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk

    A. P. Kopylov & M. V. Korobkov

  2. Pedagogical University, Slupsk, Poland

    S. P. Ponomarev

Authors
  1. A. P. Kopylov
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  2. M. V. Korobkov
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  3. S. P. Ponomarev
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Kopylov, A.P., Korobkov, M.V. & Ponomarev, S.P. Stability in the Cauchy and Morera Theorems for Holomorphic Functions and Their Spatial Analogs. Siberian Mathematical Journal 44, 99–108 (2003). https://doi.org/10.1023/A:1022068421764

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  • DOI: https://doi.org/10.1023/A:1022068421764

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