Concavity property of minimal $L^2$ integrals with Lebesgue measurable gain VIII -- partial linearity and log-convexity

Abstract

In this article, we give some necessary conditions for the concavity property of minimal $L^2$ integrals degenerating to partial linearity, a charaterization for the concavity degenerating to partial linearity for open Riemann surfaces, and some relations between the concavity property for minimal $L^2$ integrals and the log-convexity for Bergman kernels.

arXiv commentSome typos have been corrected. 37 pages, all comments are welcome! arXiv admin note: text overlap with arXiv:2211.00470