Asian Journal of Mathematics

Volume 25 (2021)

Number 3

Global perturbation potential function on complete special holonomy manifolds

Pages: 393 – 412

DOI: https://dx.doi.org/10.4310/AJM.2021.v25.n3.a4

Author

Teng Huang (School of Mathematical Sciences and the CAS Key Laboratory of Wu Wen-Tsun Mathematics, University of Science and Technology of China, Hefei, Anhui China)

Abstract

In this article, we introduce and study the notion of a complete special holonomy manifold $(X,\omega)$ which is given by a global perturbation potential function, i.e., there is a function $f$ on $X$ such that $\omega^\prime = \omega - \mathcal{L}_{\nabla_f} \omega$ is sufficiently small in $L^\infty$-norm. We establish some vanishing theorems on the $L^2$ harmonic forms under some conditions on the global perturbation potential function.

Keywords

special holonomy manifolds, $L^2$-harmonic forms, global perturbation potential function

2010 Mathematics Subject Classification

53C29, 53C38, 57R57

The full text of this article is unavailable through your IP address: 18.222.111.44

This work was supported by Nature Science Foundation of China No. 11801539, and by Postdoctoral Science Foundation of China No. 2017M621998, No. 2018T110616.

Received 19 May 2020

Accepted 9 September 2020

Published 14 March 2022