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

preprint2022arXivOpen access

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.

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

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Boundary points, minimal L2L^2L2 integrals and concavity property III -- linearity on Riemann surfaces

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