Proof of a convergence of affine Riemann surfaces to a richer one

2013/11/29 by Arnaud Chéritat, Chéritat, Arnaud
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV

paper · pdf · doi:10.48550/arxiv.1311.7520

20 pages, many figures

arxiv created 2013/11/29 · openalex publication_date 2013/11/29 · arxiv updated 2013/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a proof of a phenomenon conjectured in our former article: "Beltrami forms, affine surfaces and the Schwarz-Christoffel formula: a worked out example of straightening". We also start an abstract discussion of the notion of limits of Riemann surfaces.

Related

• Beltrami forms, affine surfaces and the Schwarz-Christoffel formula: a worked out example of straightening
• Similarity surfaces, connections, and the measurable Riemann mapping theorem
• Caratheodory convergence of log-Riemann surfaces and Euler's formula
• Ahlfors-Weill Extensions for a Class of Minimal Surfaces
• An encounter in the realm of Structural Stability between a qualitative\n theory for geometric shapes and one for the integral foliations of\n differential equations