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Algebras of differentiable functions on Riemann surfaces

Karel De Leeuw, H. Mirkil (1964)

Annales de l'institut Fourier

La structure d’une variété V indéfiniment différentiable est complètement caractérisée par l’algèbre des fonctions indéfiniment différentiables sur V . Pour des surfaces de Riemann il n’y a pas, en général, une algèbre caractérisante canonique de fonctions globalement définies. Dans ce travail l’on définit une classe dénombrable de telles algèbres. Ces algèbres sont des analogues, pour les surfaces de Riemann, des algèbres définies pour le plan par les auteurs dans “Algebras of differentiable functions...

Another algebraic proof of Weil's reciprocity

Emma Previato (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The Burchnall-Chaundy-Krichever correspondence which converts meromorphic functions on a curve into differential operators is used to interpret Weil's reciprocity as the calculation of a resultant.

Applications of Quaternionic Holomorphic Geometry to minimal surfaces

K. Leschke, K. Moriya (2016)

Complex Manifolds

In this paper we give a survey of methods of Quaternionic Holomorphic Geometry and of applications of the theory to minimal surfaces. We discuss recent developments in minimal surface theory using integrable systems. In particular, we give the Lopez–Ros deformation and the simple factor dressing in terms of the Gauss map and the Hopf differential of the minimal surface. We illustrate the results for well–known examples of minimal surfaces, namely the Riemann minimal surfaces and the Costa surface....

Embedding subsets of tori Properly into 2

Erlend Fornæss Wold (2007)

Annales de l’institut Fourier

Let 𝕋 be a complex one-dimensional torus. We prove that all subsets of 𝕋 with finitely many boundary components (none of them being points) embed properly into 2 . We also show that the algebras of analytic functions on certain countably connected subsets of closed Riemann surfaces are doubly generated.

Erratum to the paper "On the disc theorem" (Ann. Polon. Math. 55 (1991), 1-10)

Cabiria Andreian Cazacu (1992)

Annales Polonici Mathematici

Due to a technical error, part of a sentence was omitted on the top of page 8. The first line should read: “where f p k , p = a l or b l , means the number of folds of the covering ( δ k ' ' , T | , Δ l ' ' ) ending at p, i.e. covering a neighbourhood of p in a l b l without covering p itself”.

Exemples d'applications holomorphes d'indice un

Rabah Souam (1993)

Annales de l'institut Fourier

Nous construisons une famille de surfaces de Riemann hyperelliptiques, de genre variable, munies de fonctions méromorphes de degré deux et d’indice un, ce qui apporte une réponse positive à une conjecture de S. Montiel et A. Ros.

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