Solvability of a Riemann linear conjugation problem on a fractal surface.
Ricardo Abreu Blaya, Juan Bory Reyes (1998)
Extracta Mathematicae
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Ricardo Abreu Blaya, Juan Bory Reyes (1998)
Extracta Mathematicae
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Dzebisov, Kh.P. (2001)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
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V. V. Mityushev (1997)
Annales Polonici Mathematici
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The Riemann problem has been solved in [9] for an arbitrary closed Riemann surface in terms of the principal functionals. This paper is devoted to solution of the problem only for the double of a multiply connected region and can be treated as complementary to [9,1]. We obtain a complete solution of the Riemann problem in that particular case. The solution is given in analytic form by a Poincaré series.
M. V. Shapiro (1988)
Matematički Vesnik
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Gollakota V. V. Hemasundar (2011)
Annales Polonici Mathematici
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We give a complete and transparent proof of Koebe's General Uniformisation Theorem that every planar Riemann surface is biholomorphic to a domain in the Riemann sphere ℂ̂, by showing that a domain with analytic boundary and at least two boundary components on a planar Riemann surface is biholomorphic to a circular-slit annulus in ℂ.
Nadj, Djerdji F. (1981)
Publications de l'Institut Mathématique. Nouvelle Série
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Murid, Ali Hassan Mohamed, Nasser, Mohamed M.S. (2003)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Xiannan Li (2009)
Acta Arithmetica
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Krzysztof Jarosz (2012)
Annales Polonici Mathematici
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The classical Riemann Mapping Theorem states that a nontrivial simply connected domain Ω in ℂ is holomorphically homeomorphic to the open unit disc 𝔻. We also know that "similar" one-dimensional Riemann surfaces are "almost" holomorphically equivalent. We discuss the same problem concerning "similar" domains in ℂⁿ in an attempt to find a multidimensional quantitative version of the Riemann Mapping Theorem
O. Richter, C. Klein (1997)
Banach Center Publications
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1. Introduction. It is well known that methods of algebraic geometry and, in particular, Riemann surface techniques are well suited for the solution of nonlinear integrable equations. For instance, for nonlinear evolution equations, so called 'finite gap' solutions have been found by the help of these methods. In 1989 Korotkin [9] succeeded in applying these techniques to the Ernst equation, which is equivalent to Einstein's vacuum equation for axisymmetric stationary fields. But, the...
Keiko Narita, Kazuhisa Nakasho, Yasunari Shidama (2016)
Formalized Mathematics
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In this article, the definitions and basic properties of Riemann-Stieltjes integral are formalized in Mizar [1]. In the first section, we showed the preliminary definition. We proved also some properties of finite sequences of real numbers. In Sec. 2, we defined variation. Using the definition, we also defined bounded variation and total variation, and proved theorems about related properties. In Sec. 3, we defined Riemann-Stieltjes integral. Referring to the way of the article [7],...
Kazuhisa Nakasho, Keiko Narita, Yasunari Shidama (2016)
Formalized Mathematics
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In this article, the basic existence theorem of Riemann-Stieltjes integral is formalized. This theorem states that if f is a continuous function and ρ is a function of bounded variation in a closed interval of real line, f is Riemann-Stieltjes integrable with respect to ρ. In the first section, basic properties of real finite sequences are formalized as preliminaries. In the second section, we formalized the existence theorem of the Riemann-Stieltjes integral. These formalizations are...
Masatoshi Suzuki (2013)
Acta Arithmetica
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We introduce a family of deformations of the Riemann xi-function endowed with two continuous parameters. We show that it has rich analytic structure and that its conjectural (mild) zero-free region for some fixed parameter is a sufficient condition for the Riemann hypothesis to hold for the Riemann zeta function.
Herbert Schröder (1988-1989)
Séminaire de théorie spectrale et géométrie
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N. Paul Schembari, Michael Schramm (1990)
Colloquium Mathematicae
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Dinu, Liviu Florin, Dinu, Mariana Ileana (2004)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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