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WEIGHTED L2 HARMONIC 1-FORMS AND THE TOPOLOGY AT INFINITY OF COMPLETE NONCOMPACT WEIGHTED MANIFOLDS
- Authors
- Seo, Keomk Yo; Yun, Gabjin
- Issue Date
- Dec-2023
- Publisher
- Tohoku University, Mathematical Institute
- Keywords
- topology at infinity; weighted harmonic forms; Weighted manifolds; weighted Sobolev inequality
- Citation
- Tohoku Mathematical Journal, v.75, no.4, pp 509 - 526
- Pages
- 18
- Journal Title
- Tohoku Mathematical Journal
- Volume
- 75
- Number
- 4
- Start Page
- 509
- End Page
- 526
- ISSN
- 0040-8735
- 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 L2 f f -harmonic 1-forms on a complete noncompact weighted manifold supporting the weighted Sobolev inequality.
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