Concavity property of minimal L² integrals with Lebesgue measurable gain VIII -- partial linearity and log-convexity

2023/07/14 by Shijie Bao, Bao, Shijie, Qi’an Guan +3
Mathematics · #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2307.07112

openalex publication_date 2023/07/14 · openalex created_date 2023/07/18 · openalex updated_date 2026/07/28

Abstract

In this article, we give some necessary conditions for the concavity property of minimal L² 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 L² integrals and the log-convexity for Bergman kernels.

Related

• Concavity property of minimal L² integrals with Lebesgue measurable gain
• Concavity property of minimal L² integrals with Lebesgue measurable gain II
• Concavity property of minimal L² integrals with Lebesgue measurable gain III: open Riemann surfaces
• Concavity property of minimal L² integrals with Lebesgue measurable gain IV: product of open Riemann surfaces
• Concavity property of minimal L² integrals with Lebesgue measurable gain VII -- Negligible weights