New trends in complex analysis and potential theory

Información del proyecto

Identificador del acuerdo de subvención: INTAS-1999-00089

Proyecto cerrado

Fecha de inicio 1 Mayo 2000

Fecha de finalización 30 Abril 2003

Financiado con arreglo a

• International Association for the promotion of cooperation with scientists from the independent states of the former Soviet Union (INTAS), 1993-

Coste total

Sin datos

Aportación de la UE

€ 149 630,00

Coordinado por

University of Joensuu
Finland

Objetivo

The interplay between potential theory, value distribution theory, complex dynamics and geometric function theory has been decisive for several deep results recently. The overall objective is
(1) to conduct active, co-ordinated search for such interplay ideas;
(2) Evaluating consequences of these ideas aims;
(3) to extend the present knowledge in the above and related Fields such as;
(4) complex differential equations and complex function spaces. Practical consequences will be approached by;
(5) investigating the intersection of value distribution theory and applied mathematics and by (6) considering applications to control theory and optimisation;
(7) All teams will be active in doctoral and post-doctoral training, including opening of internal workshops for outsiders.

Scientific research to be done: In potential theory, the standard non-linear potential theory (corresponding to quasi-regular mappings) will be extended to the non-linear pluripotential theory (corresponding to functions of several complex variables). Classical subharmonic functions will also be studied, in relation to the value distribution theory. In particular, the celebrated star function idea will be extended by providing a general scheme of constructing operators preserving subharmonicity. Studies in fine potential theory aim to attack several difficult problems in analysis.

In value distribution theory, a key idea is to study locations of a-points of meromorphic functions, similarly as to the classical theory describing the quantities of a-points. This will be approached by the method of gamma-lines and by studying Fourier coefficients of logarithms of meromorphic functions. Applications of gamma-lines into physics and environmental problems will also be studied. To extend classical plane results to the unit disk, order considerations of meromorphic functions of slow growth will be performed, as well as studies of the link between normal families and value distribution theory.

In complex dynamics, the dynamics of transcendental functions will be investigated by looking several questions previously well understood for rational functons. A systematic investigation will be made on wandering and Baker domains, including the interplay between complex dynamics and complex differential equations. In the latter field, applying the location studies above will perform considerations on locations of a-points of solutions. Normal family arguments and complex function space ideas will be applied to complex differential equations.

In geometric function theory, the present knowledge of quasi conformal and quasi regular mappings will be extended to a theory of multi-valued quasi regular mappings. Local structure considerations needed here will be applied to finding extreme metrics and moduli in non-orientable Riemannian manifolds. Moreover, similar extremal problem ideas in univalent functions will be applied to approximation theory.

Complex function spaces and operator theory will be studied to build up a strong bridge to value distribution theory in addition to the relation with the star function ideas. Extreme problem ideas similar as to described above may be combined with control theoretic and optimisation methods to obtain new important extremal problem results for linear functionals.

Dissemination of research results: All research results will be published in high-level refereed journals and, if relevant, as monographs through international publishers. Before published, the results will be made accessible for the outside mathematical community by electronic communication.

Ámbito científico (EuroSciVoc)

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Programa(s)

• IC-INTAS - International Association for the promotion of cooperation with scientists from the independent states of the former Soviet Union (INTAS), 1993-

Tema(s)

• 2 - Mathematics, Telecommunications, Information Technologies
• OPEN - OPEN Call

Convocatoria de propuestas

Datos no disponibles

Régimen de financiación

Datos no disponibles

Coordinador

University of Joensuu

• Aportación de la UE: Sin datos
• Dirección: Yliopistokatu 7 ; 80101 Joensuu ; Finlandia
• Coste total: Sin datos

Participantes (8)

Bayerische Julius-Maximilians-Universität Würzburg

Alemania

• Aportación de la UE: Sin datos
• Dirección: Am Hubland ; 97074 Würzburg
• Coste total: Sin datos

Christian-Albrechts-Universität zu Kiel

Alemania

• Aportación de la UE: Sin datos
• Dirección: Ludewig-Meyn-Strasse 4 ; 24098 Kiel
• Coste total: Sin datos

Department of Pure and Applied Mathematics

Armenia

• Aportación de la UE: Sin datos
• Dirección: Hastatian Street 7 ; 375014 Erevan
• Coste total: Sin datos

Lviv State University

Ucrania

• Aportación de la UE: Sin datos
• Dirección: Universytetska 1 ; 290602 Lviv
• Coste total: Sin datos

National Academy of Sciences of Ukraine

Ucrania

• Aportación de la UE: Sin datos
• Dirección: Tereshchenkivska 3 ; 252601 Kiev
• Coste total: Sin datos

National Academy of Sciences of Ukraine

Ucrania

• Aportación de la UE: Sin datos
• Dirección: Prospekt Lenina 47 ; 31016401 Kharkov
• Coste total: Sin datos

Saratov State University

Rusia

• Aportación de la UE: Sin datos
• Dirección: Astrakhanskaya 83 ; 410026 Saratov
• Coste total: Sin datos

University of Helsinki

Finlandia

• Aportación de la UE: Sin datos
• Dirección: Yliopistonkatu 15 ; 00014 Helsinki
• Coste total: Sin datos