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

Qi'an Guan; Zhitong Mi

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

Complex Variables 2021-06-14 v2

Authors: Qi'an Guan , Zhitong Mi

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.

Keywords

minimal l2 integrals multiplier ideal sheaves stein manifolds concavity l2 extension

Cite

@article{arxiv.2106.05089,
  title  = {Concavity of minimal $L^2$ integrals related to multipler ideal sheaves},
  author = {Qi'an Guan and Zhitong Mi},
  journal= {arXiv preprint arXiv:2106.05089},
  year   = {2021}
}

Comments

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

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