# Georgii Dmitrievic Suvorov

### Born: 19 May 1919 in Saratov, Russia

Died: 12 October 1984 in Donetske, Ukraine

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**Georgii Dmitrievich Suvorov**was born in Saratov, in western Russia on the Volga River. He studied at Tomsk University, the first Siberian university which had been founded in 1888, graduating in 1941. Of course, by this time World War II was deeply affecting Russia since German troops had invaded the Soviet Union on 22 June 1941 as part of Operation Barbarossa. After graduating, Suvorov served in the army and remained in active service until the end of the war in 1945. He was awarded several medals for bravery during his years of service. After being demobilized, Suvorov tried to continue his career along the lines that he had been intending before the war interrupted his studies. He returned to Tomsk University where he undertook research with Pavel Parfen'evich Kufarev as his advisor. In fact Kufarev, Head of the Departments of Analysis and Theory of Functions and an expert on the theory of functions of a complex variable and its applications, was the only possible research supervisor at Tomsk University being the only professor of mathematics in Siberia at the time. Suvorov completed work on his Master's Thesis (equivalent to a Ph.D.) in 1951 and, at that time was appointed as an assistant at Tomsk University.

At Tomsk, Suvorov was soon promoted from assistant to lecturer. His outstanding contributions then led to him being made professor and Head of the Department of Theory of Functions at the University of Tomsk. In 1961 he was awarded his doctorate (equivalent to a D.Sc.) for his thesis

*Main properties of certain classes of topological mappings of plane domains with variable boundaries*. He continued to teach at Tomsk University until 1965 when he was elected to Ukrainian Academy of Sciences and, in the following year, took up his appointment as Head of the Department of the Theory of Functions at the Donetsk Computing Centre. He continued in this role after it became the Institute of Applied Mathematics and Mechanics of the Ukrainian Academy of Sciences.

Suvorov made major contributions to the theory of functions. He worked, in particular, on the theory of topological and metric mappings on 2-dimensional space. Another area on which Suvorov worked was the theory of conformal mappings and quasi-formal mappings. His results in this area, mostly from the late 1960s when he was at Donetsk, are of particular significance. He extended Lavrent'ev's results in this area, in particular Lavrent'ev's stability and differentiability theorems, to more general classes of transformations. One of the many innovations in Suvorov's work was new methods which he introduced to help in the understanding of metric properties of mappings with bounded Dirichlet integral. In [6] his main contributions are described as follows:-

Let us end this biography by looking briefly at some of the monographs that Suvorov wrote. In 1965 he publishedG D Suvorov's researches during the last decade are interesting and significant; they open new paths in the theory of functions and raise new problems. The lucidity and accuracy are characteristic of him, the geometrical aspect distinctly predominates. In particular, he has proved a deep and interesting theorem that gives sufficient conditions for the coincidence of limit sets for space mappings of a very general class under very general conditions. This important result served as a source for the investigations of principally new character: The above-mentioned theorem cannot be explained even in the case of conformal mappings in the framework of the usual theory of boundary correspondence by prime ends since the limit sets with respect to two sequences of points that converge to the same prime end may be different. In connection with this, G D Suvorov posed the problem whether there exist conformal invariant compactifications of a simply connected plane domain(in the first instance, metrizable)different from the Carathéodory(and from the "trivial" one from the point of view of the known theory of the one-point and the Stone-Čech compactifications), and about the description of all such compactifications. As it turns out, infinitely many such conformal-invariant compactifications, metrizable as well as nonmetrizable, exist. Thus the new formulation of the problem is interesting and useful; each new conformal-invariant compactification furnishes new boundary properties of conformal mappings. G D Suvorov and his students have constructed and studied two entirely new complete lattices of conformal-invariant compactifications. He also succeeded in obtaining a description of all conformal-invariant compactifications of a simply connected plane domain; moreover, it turns out that the family of all such compactifications constitutes a complete lattice.

*Families of plane topological mappings*(Russian). Petru Caraman begins a review with these words:-

In 1981 Suvorov publishedThis monograph contains the results of about twenty of the author's preceding works and is directed to specialists in the theory of functions of one complex variable, and particularly to those who deal with quasiconformal mappings. The book is divided into two parts. In the second part, which is completely original, the author studies the boundary correspondence by a sequence of homeomorphisms of two sequences of domains converging to their kernels

*The metric theory of prime ends and boundary properties of plane mappings with bounded Dirichlet integrals*(Russian). A E Eremenko writes:-

A collaboration between Suvorov and Oleg V Ivanov led to a number of joint papers which formed the basis for their joint monographThe book contains a new construction of the theory of prime ends of simply connected plane domains based on the notion of completion of a metric space. Some applications of this theory to the study of mappings with bounded Dirichlet integral are also described. The author attempts to separate precisely the metric aspect of the theory from the topological.

*Complete lattices of conformally invariant compactifications of a domain*(Russian). A review, again by Petru Caraman, begins:-

Suvorov's final two monographs were published in 1985 and 1986 after his death in 1984. The first wasCaratheodory(1913)introduced for the first time a compactification of a simply connected domain by means of boundary elements, which he called "prime ends", and proved that they are conformal invariants. The authors obtain a whole set of conformally invariant compactifications(metrizable and nonmetrizable), which is proved to form a complete lattice. They also consider the sublattice of stable conformally invariant compactifications, which is also complete. Finally, they give some applications in potential theory(Dirichlet problem).

*The generalized "length and area principle" in mapping theory*(Russian) and the second

*Prime ends and sequences of plane mappings*(Russian). This final monograph continues to develop the topics considered in his two earlier monographs

*Families of plane topological mappings*(1965) and

*The metric theory of prime ends and boundary properties of plane mappings with bounded Dirichlet integrals*(1981).

In addition to his academic work, Suvorov also made important contributions to [6]:-

... the general problems of national education and musical training.

**Article by:** *J J O'Connor* and *E F Robertson*

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**List of References** (6 books/articles)

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