CONCAVITY PROPERTY OF MINIMAL INTEGRALS WITH LEBESGUE MEASURABLE GAIN
Qi’an Guan, 正樹 柏原
Abstract
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.
Topics & Concepts
MathematicsLebesgue integrationMultiplier (economics)SubharmonicProperty (philosophy)Pure mathematicsLebesgue measureCharacterization (materials science)Ideal (ethics)Mathematical analysisNonlinear systemMaterials scienceMacroeconomicsEconomicsNanotechnologyEpistemologyPhysicsQuantum mechanicsPhilosophyGeometry and complex manifoldsHolomorphic and Operator TheoryGeometric Analysis and Curvature Flows