Concavity property of minimal $L^2$ integrals with Lebesgue measurable gain

Qi'an Guan; Zheng Yuan

Concavity property of minimal $L^2$ integrals with Lebesgue measurable gain

Complex Variables 2022-11-02 v1

Authors: Qi'an Guan , Zheng Yuan

Abstract

In this article, we present a concavity property of the minimal $L^2$ integrals related to multiplier ideal sheaves with Lebesgue measurable gain. As applications, we give necessary conditions for our concavity degenerating to linearity, characterizations for 1-dimensional case, and a characterization for the holding of the equality in optimal $L^2$ extension problem on open Riemann surfaces with weights may not be subharmonic.

Keywords

minimal L^2 integrals lebesgue measurable gain multiplier ideal sheaves concavity optimal L^2 extension riemann surfaces

Cite

@article{arxiv.2209.03637,
  title  = {Concavity property of minimal $L^2$ integrals with Lebesgue measurable gain},
  author = {Qi'an Guan and Zheng Yuan},
  journal= {arXiv preprint arXiv:2209.03637},
  year   = {2022}
}

Comments

65pages, this is a modified version of the paper we uploaded to Researchgate, see https://www.researchgate.net/publication/353794984

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