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- Title
CONCAVITY PROPERTY OF MINIMAL $L^{2}$ INTEGRALS WITH LEBESGUE MEASURABLE GAIN.
- Authors
GUAN, QI'AN; YUAN, ZHENG
- 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.
- Subjects
LEBESGUE integral; RIEMANN surfaces; RIEMANN-Hilbert problems; SHEAF theory; INTEGRALS
- Publication
Nagoya Mathematical Journal, 2023, Vol 252, p842
- ISSN
0027-7630
- Publication type
Article
- DOI
10.1017/nmj.2023.12