Boundary points, minimal $L^2$ integrals and concavity property III -- linearity on Riemann surfaces

Abstract

In this article, we consider a modified version of minimal $L^2$ integrals on sublevel sets of plurisubharmonic functions related to modules at boundary points, and obtain a concavity property of the modified version. As an application, we give a characterization for the concavity degenerating to linearity on open Riemann surfaces.

arXiv comment49 pages, all comments are welcome. arXiv admin note: substantial text overlap with arXiv:2203.07723