Vekua method

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in the theory of infinitesimal deformations

A method which can be applied to the case when certain quantities which characterize the deformation of surfaces with positive Gaussian curvature $ K $ are, in a conjugate-isothermal parametrization, generalized analytic functions (cf. Generalized analytic function). This makes it possible to reduce the study of the deformation of surfaces with variable $ K > 0 $ to a definite problem concerning surfaces with $ K = \textrm{ const } > 0 $, whose infinitesimal deformations (cf. Infinitesimal deformation) are described by ordinary analytic functions, thus establishing a far-reaching analogy between the properties of deformations of surfaces with variable and constant positive Gaussian curvature.


[1] I.N. Vekua, "Generalized analytic functions" , Pergamon (1962) (Translated from Russian)
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Vekua method. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article