Concavity of minimal $L^2$ integrals related to multipler ideal sheaves

Abstract

In this note, we present the concavity of the minimal $L^2$ integrals related to multiplier ideals sheaves on Stein manifolds. As applications, we obtain a necessary condition for the concavity degenerating to linearity, a characterization for 1-dimensional case, and a characterization for the equality in 1-dimensional optimal $L^2$ extension problem to hold.

arXiv comment56 pages. Some typos are corrected. For convenience of the reader, we simplify the statements in Corollary 1.10

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• Twisted version of Strong openness property in $L^p$