Finiteness and vanishing results on weighted Poincare inequality of complete manifolds

Kwan-hang Lam

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arXiv · 0711.0924

Finiteness and vanishing results on weighted Poincare inequality of complete manifolds

Kwan-hang Lam

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Abstract

We study manifolds satisfying a weighed Poincare inequality, which was first introduced by Li-Wang. We generalized one of their results by relaxing the Ricci curvature bound condition only being satisfied outside a compact set and established a finitely many ends result. We proved a vanishing result for $L^2$ harmonic 1-form provided that the weight function $ρ$ is of sub-quadratic growth of the distance function.

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BibTeX RIS

Kwan-hang Lam. 2007-11-06. Finiteness and vanishing results on weighted Poincare inequality of complete manifolds. https://arxiv.org/abs/0711.0924

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