Boundary points, minimal $L^2$ integrals and concavity property IV -- fibrations over open Riemann surfaces

TL;DR

This paper investigates minimal $L^2$ integrals at boundary points on fibrations over open Riemann surfaces, providing a characterization of when the associated concavity property becomes linear.

Contribution

It introduces a new characterization for the degeneracy of the concavity property of minimal $L^2$ integrals in the context of fibrations over open Riemann surfaces.

Findings

Characterization of linearity degeneration in concavity of minimal $L^2$ integrals

Analysis of boundary point modules on fibrations over Riemann surfaces

Insights into the structure of minimal $L^2$ integrals in complex geometry

Abstract

In this article, we consider the minimal $L^2$ integrals related to modules at boundary points on fibrations over open Riemann surfaces, and present a characterization for the concavity property of the minimal $L^2$ integrals degenerating to linearity.