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A sharp estimate for the bottom of the spectrum of the laplacian on kähler manifolds

Ovidiu Munteanu University of California

Differential Geometry mathscidoc:1609.10136

Journal of Differential Geometry, 83, (1), 163-187, 2009
On a complete noncompact K¨ahler manifold we prove that the bottom of the spectrum for the Laplacian is bounded from above by m2 if the Ricci curvature is bounded from below by −2(m+1). Then we show that if this upper bound is achieved then either the manifold is connected at infinity or it has two ends and in this case it is diffeomorphic to the product of the real line with a compact manifold and we determine the metric.
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@inproceedings{ovidiu2009a,
  title={A SHARP ESTIMATE FOR THE BOTTOM OF THE SPECTRUM OF THE LAPLACIAN ON  Kähler MANIFOLDS},
  author={Ovidiu Munteanu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911195538576823793},
  booktitle={Journal of Differential Geometry},
  volume={83},
  number={1},
  pages={163-187},
  year={2009},
}
Ovidiu Munteanu. A SHARP ESTIMATE FOR THE BOTTOM OF THE SPECTRUM OF THE LAPLACIAN ON Kähler MANIFOLDS. 2009. Vol. 83. In Journal of Differential Geometry. pp.163-187. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911195538576823793.
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