Finiteness and vanishing results on weighted Poincare inequality of complete manifolds

Details Finiteness and vanishing results on weighted Poincare inequality of complete manifolds Finiteness and vanishing results on weighted Poincare inequality of complete manifolds

2007-11-06

arxiv.org/abs/0711.0924v1

Mathematics

Differential Geometry

Scientific paper

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 $\rho$ is of sub-quadratic growth of the distance function.

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