Mathematische Zeitschrift

, Volume 291, Issue 1–2, pp 279–302 | Cite as

A non-Archimedean Ohsawa–Takegoshi extension theorem

  • Matthew StevensonEmail author


We prove an Ohsawa–Takegoshi-type extension theorem on the Berkovich closed unit disc over certain non-Archimedean fields. As an application, we establish a non-Archimedean analogue of Demailly’s regularization theorem for quasisubharmonic functions on the Berkovich unit disc.



I would like to thank my advisor, Mattias Jonsson, for suggesting the problem and for his invaluable help, guidance, and support. I would also like to thank Kiran Kedlaya, Jérôme Poineau, and Daniele Turchetti for helpful conversations regarding Lemma 2.1. I am grateful to Takumi Murayama and Emanuel Reinecke for their many comments on a previous draft. Finally, I would like to thank the anonymous referee for their many helpful comments, and for pointing out an error in a previous version. This work was partially supported by NSF grant DMS-1600011.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

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