Work

Asymptotic expansions of $L^2$-extension indices and curvature positivity

Year: 2026

Type: preprint

Abstract: In this paper, we prove an asymptotic expansion of the $L^2$-extension index of a smooth Hermitian metric on a holomorphic vector bundle, in which the Chern curvature appears as the second-order coefficient. By using this expansion, we show in a unified way that there is an equivalence between how sharp the $L^2$-extension is and how positive or negative the curvature is. We also introduce a new notion of $q$-$L^2$-extension indices and investigate partial positivity and flatness in terms of these indices.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.15088

Author: Inayama, Takahiro

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

Award: New development of geometric complex analysis based on L2 estimates and L2 extension theorems

OpenAlex ID: W7213251676

Cites:

Cited by:

Related to: 10