$L^{2}$ vanishing theorem on some K\"{a}hler manifolds

Teng Huang

$L^{2}$ vanishing theorem on some K\"{a}hler manifolds

Differential Geometry 2019-07-23 v2

Authors: Teng Huang

Abstract

Let $E$ be a Hermitian vector bundle over a complete K\"{a}hler manifold $(X,\omega)$ , $\dim_{\mathbb{C}}X=n$ , with a $d$ (bounded) K\"{a}hler form $\omega$ , $d_{A}$ be a Hermitian connection on $E$ . The goal of this article is to study the $L^{2}$ -Hodge theory on the vector bundle $E$ . We extend the results of Gromov's \cite{Gro} to the Hermitian vector bundle. At last, as an application, we prove a gap result for Yang-Mills connection on the bundle $E$ over $X$ .

Keywords

kähler manifold l2 vanishing theorem hermitian vector bundle hodge theory yang-mills connection

Cite

@article{arxiv.1811.10772,
  title  = {$L^{2}$ vanishing theorem on some K\"{a}hler manifolds},
  author = {Teng Huang},
  journal= {arXiv preprint arXiv:1811.10772},
  year   = {2019}
}

Comments

We would like to thank the anonymous referee pointed out that we can study the nonvanishing theorem in the small enough $L^{\infty}$-norm case. To appear in Isr. J. Math

$L^{2}$ vanishing theorem on some K\"{a}hler manifolds

Abstract

Keywords

Cite

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