WEIGHTED L²HARMONIC 1-FORMS AND THE TOPOLOGY AT INFINITY OF COMPLETE NONCOMPACT WEIGHTED MANIFOLDS

TOHOKU MATHEMATICAL JOURNAL（2023）

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摘要

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(f )(2)f-harmonic 1-forms on a complete noncompact weighted manifold supporting the weighted Sobolev inequality.

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关键词

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

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WEIGHTED L2 HARMONIC 1-FORMS AND THE TOPOLOGY AT INFINITY OF COMPLETE NONCOMPACT WEIGHTED MANIFOLDS

WEIGHTED L²HARMONIC 1-FORMS AND THE TOPOLOGY AT INFINITY OF COMPLETE NONCOMPACT WEIGHTED MANIFOLDS