Main scientific activity
V.Ya. Gutlyansky is one of the leading scientists in the field of complex analysis. His significant achievement is the development of the Löwner-Kufarev method, plane and variation methods for conformal and quasiconformal mappings. On this basis, he obtained solutions to the general problem of distortion and rotation, the problem of the radius of starlikeness, exact two-sided estimates of the modulus, and others. Together with his students, he proved theorems on the existence of generalized solutions to boundary value problems of Dirichlet, Neumann, Poincaré, Hilbert, and Riemann for the Beltrami equation and equations of mathematical physics in anisotropic and inhomogeneous media. In a series of works written jointly with well-known scientists from the USA, Finland, and Japan, an exact solution to the famous rotation problem of F. John for bilipschitz and quasiconformal deformations of the complex plane was presented, and a theorem on the differentiability of mappings was established, encompassing the classical result of Teichmüller-Wittich-Belinskii.
