English

A Hilbert bundle approach to the sharp strong openness theorem and the Ohsawa-Takegoshi extension theorem

Complex Variables 2024-02-27 v3 Algebraic Geometry Differential Geometry

Abstract

The following paper is around parts of the first named author's thesis. We discuss (what we call) a Hilbert bundle approach to complex Brunn-Minkowski theory and obtain a general monotonicity theorem. As two applications, we prove a generalization of Guan's sharp strong openness theorem and a sharp Ohsawa-Takegoshi extension theorem. A second proof of Guan-Zhou's strong openness theorem using a Donnelly-Fefferman estimate is also given.

Keywords

Cite

@article{arxiv.2111.08422,
  title  = {A Hilbert bundle approach to the sharp strong openness theorem and the Ohsawa-Takegoshi extension theorem},
  author = {Tai Terje Huu Nguyen and Xu Wang},
  journal= {arXiv preprint arXiv:2111.08422},
  year   = {2024}
}

Comments

New version, accepted by Contemporary Mathematics