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Petersburg Department of Steklov Institute of Mathematics

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PREPRINT 3/1997

А. Ю. Солынин
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Модули и экстремально-метрические проблемы

This preprint was accepted February, 1997.

Contact: ` A. Yu. Solynin `

Abstract:

The paper deals with problems on an extremal partition of a finite
Riemann surface into configurations of a special topological form.
The foundations of this theory, closely relative to the theory of
quadratic differentials, were established by J. A. Jenkins.
A lot of important
results were also proved by K. Strebel, H. Renelt, G. V. Kuz'mina,
and others. The present paper includes a detailed exposition of this
theory for the problems associated with quadratic differentials that
have poles at most second order with circular and radial structure
of trajectories. In particular, we begin by proving the existence and
uniqueness theorems for the extremal configurations then develop
the theory of differentiability for the weighted sum of extremal moduli.
Bibliography--71.

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