Results on a weighted Poincaré inequality of complete manifolds

Lam, Kwan-hang

doi:10.1090/S0002-9947-10-04894-4

Results on a weighted Poincaré inequality of complete manifolds
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by Kwan-hang Lam PDF

Trans. Amer. Math. Soc. 362 (2010), 5043-5062 Request permission

Abstract:

We study manifolds satisfying a weighted Poincaré inequality, which was first introduced by Li and Wang. We generalized their result by relaxing the Ricci curvature bound condition only being satisfied outside a compact set and established a finitely many ends result. We also proved a vanishing result for an $L^2$ harmonic 1-form provided that the weight function $\rho$ is of sub-quadratic growth of the distance function, which generalized the Li-Wang result on manifolds with a positive spectrum.

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