A converse of Hörmander’s L 2-estimate and new positivity notions for vector bundles

Genki Hosono, Takahiro Inayama

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We study conditions of Hörmander’s L2-estimate and the Ohsawa-Takegoshi extension theorem. Introducing a twisted version of the Hörmander-type condition, we show a converse of Hörmander L2-estimate under some regularity assumptions on an n-dimensional domain. This result is a partial generalization of the 1-dimensional result obtained by Berndtsson (1998). We also de_ne new positivity notions for vector bundles with singular Hermitian metrics by using these conditions. We investigate these positivity notions and compare them with classical positivity notions.

Original languageEnglish
Pages (from-to)1745-1756
Number of pages12
JournalScience China Mathematics
Issue number8
Publication statusPublished - Aug 2021


  • 32A10
  • 32L10
  • L-estimate
  • Ohsawa-Takegoshi L-extension theorems
  • singular Hermitian metrics


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