H. Cartan's theory for Riemann surfaces
Xianjing Dong
TL;DR
This paper extends Cartan's theory of holomorphic curves to general open Riemann surfaces, introduces a vanishing theorem for jet differentials, and proves a version of Bloch's theorem for these surfaces.
Contribution
It generalizes Cartan's theory to broader classes of Riemann surfaces and establishes new vanishing and Bloch-type theorems.
Findings
Extended Cartan's theory to open Riemann surfaces
Proved a vanishing theorem for jet differentials
Established a Bloch's theorem for Riemann surfaces
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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Meromorphic and Entire Functions · Geometry and complex manifolds