English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The Geometric Shafarevich Conjecture and the Theorem of de Franchis state thefiniteness of the number of certain holomorphic objects on closed or puncturedRiemann surfaces. The analog of these kind of theorems for Riemann surfaces ofsecond kind is an estimate of the number of irreducible holomorphic objects upto homotopy (or isotopy, respectively). This analog can be interpreted as aquantitatve statement on the limitation for Gromov's Oka principle. For anyfinite open Riemann surface $X$ (maybe, of second kind) we give an effectiveupper bound for the number of irreducible holomorphic mappings up to homotopyfrom $X$ to the twice punctured complex plane, and an effective upper bound forthe number of irreducible holomorphic torus bundles up to isotopy on such aRiemann surface. The bound depends on a conformal invariant of the Riemannsurface. If $X_{\sigma}$ is the $\sigma$-neighbourhood of a skeleton of an openRiemann surface with finitely generated fundamental group, then the number ofirreducible holomorphic mappings up to homotopy from $X_{\sigma}$ to the twicepunctured complex plane grows exponentially in $\frac{1}{\sigma}$.

Riemann surfaces of second kind and effective finiteness theorems