2023 Weighted $L^2$ harmonic 1-forms and the topology at infinity of complete noncompact weighted manifolds
Keomkyo Seo, Gabjin Yun
Tohoku Math. J. (2) 75(4): 509-526 (2023). DOI: 10.2748/tmj.20220513

Abstract

In this paper, we prove that a complete noncompact weighted manifold supporting the weighted Sobolev inequality has at least linear weighted volume growth. We also obtain vanishing results and finiteness theorems for the weighted $L^2_f$ $f$-harmonic 1-forms on a complete noncompact weighted manifold supporting the weighted Sobolev inequality.

Citation

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Keomkyo Seo. Gabjin Yun. "Weighted $L^2$ harmonic 1-forms and the topology at infinity of complete noncompact weighted manifolds." Tohoku Math. J. (2) 75 (4) 509 - 526, 2023. https://doi.org/10.2748/tmj.20220513

Information

Published: 2023
First available in Project Euclid: 12 December 2023

MathSciNet: MR4677753
Digital Object Identifier: 10.2748/tmj.20220513

Subjects:
Primary: 53C21
Secondary: 53C20 , 58J05

Keywords: topology at infinity , weighted harmonic forms , Weighted manifolds , weighted Sobolev inequality

Rights: Copyright © 2023 Tohoku University

Vol.75 • No. 4 • 2023
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