Inhaltszusammenfassung

Conformal mappings, which are bijective and complex differentiable, transfer potential functions fromone domain in the complex number plane to another. Therefore, it is also interesting for applications if there is a conformal mapping from a given domain to a domain on which the potential functions can be easily described, in particular, the unit disc. In 1851, Bernhard Riemann (1826– 1866) stated that such a mapping always exists if the initial domain is simply connected, i.e., has no holes....Conformal mappings, which are bijective and complex differentiable, transfer potential functions fromone domain in the complex number plane to another. Therefore, it is also interesting for applications if there is a conformal mapping from a given domain to a domain on which the potential functions can be easily described, in particular, the unit disc. In 1851, Bernhard Riemann (1826– 1866) stated that such a mapping always exists if the initial domain is simply connected, i.e., has no holes. However, he did not provide an explicit representation for this mapping.As early as the winter semester 1863/64, Franz/Franciszek Mertens (1840–1927) confronted Riemann’s existence statement with the fact that the effective determination of a conformal mapping of “the area of a disc onto the area of a plane straight-sided triangle [...] at the present time [...] seems to exceed the powers of analysis”. Hermann Amandus Schwarz (1843–1921) took on this problem and solved it. However, when he wanted to publish his result a few years later, he had to learn that Elwin Bruno Christoffel (1829–1900) had also solved the problem in the meantime. Since Schwarz had been offered the position of Christoffel’s successor at the Polytechnic in Zürich, the question of priority was a somewhat delicate issue. Ultimately, Schwarz resolved it with the help of his academic teacher KarlWeierstraß (1815–1897).» weiterlesen» einklappen

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