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