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Results on a weighted Poincaré inequality of complete manifolds
Author(s):
Kwan-hang
Lam
Journal:
Trans. Amer. Math. Soc.
362
(2010),
5043-5062.
MSC (2000):
Primary 54C40, 14E20;
Secondary 46E25, 20C20
Posted:
May 17, 2010
MathSciNet review:
2657671
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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  harmonic 1-form provided that the weight function  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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Additional Information:
Kwan-hang
Lam
Affiliation:
Division of Mathematics, National Center for Theoretical Sciences (South), Department of Mathematics, National Cheng-Kung University, Tainan 701, Taiwan
Email:
khlam@alumni.uci.edu
DOI:
10.1090/S0002-9947-10-04894-4
PII:
S 0002-9947(10)04894-4
Keywords:
Weighted Poincar\'e inequality,
parallel forms
Received by editor(s):
December 17, 2007
Posted:
May 17, 2010
Additional Notes:
This research was partially supported by NSF grant \#0503735 and NSC grant 96-2115-M-006-017 of the ROC
Copyright of article:
Copyright
2010,
American Mathematical Society
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