H. Cartan's theory for Riemann surfaces

2020/10/14 by Xianjing Dong, Dong, Xianjing
Mathematics · #30D35 #32H30 #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2010.06965

openalex publication_date 2020/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize the H. Cartan's theory of holomorphic curves for a general open Riemann surface. Besides, a vanishing theorem for jet differentials and a Bloch's theorem for Riemann surfaces are obtained.

Citations

• Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I

Related

• On Cartan's second main theorems for holomorphic curves on M-punctured complex planes
• The Second Main Theorem in the hyperbolic case
• Note about holomorphic maps on a compact Riemann surface
• Surfaces de Riemann compactes, courbes algébriques complexes et leurs Jacobiennes
• Holomorphic curves whose domains are Riemann surfaces