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Manifolds with a weighted Poincaré inequality


Authors: Nguyen Thac Dung and Chiung-Jue Anna Sung
Journal: Proc. Amer. Math. Soc. 142 (2014), 1783-1794
MSC (2010): Primary 53C40
DOI: https://doi.org/10.1090/S0002-9939-2014-11971-X
Published electronically: February 14, 2014
MathSciNet review: 3168484
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Abstract: We study complete manifolds satisfying a weighted Poincaré type property. We establish a splitting and vanishing theorem for $ L^2$ harmonic forms provided that the weight function $ \rho $ is of exponential growth of the distance function. Our theory generalizes the results of Li-Wang, Lam and Chen-Sung.


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Additional Information

Nguyen Thac Dung
Affiliation: Department of Mathematics, National Tsing Hua University, Kuang-Fu Road, Hsinchu, Taiwan 30013
Email: dungmath@yahoo.co.uk

Chiung-Jue Anna Sung
Affiliation: Department of Mathematics, National Tsing Hua University, Kuang-Fu Road, Hsinchu, Taiwan 30013
Email: cjsung@math.nthu.edu.tw

DOI: https://doi.org/10.1090/S0002-9939-2014-11971-X
Received by editor(s): June 8, 2012
Published electronically: February 14, 2014
Additional Notes: The first author was partially supported by the grant NAFOSTED 101.01-2011.13
The second author was partially supported by the NSC
Communicated by: Lei Ni
Article copyright: © Copyright 2014 American Mathematical Society