Existence of the spectral gap for elliptic operators

Feng-Yu Wang Department of Mathematics, Beijing Normal University

TBD mathscidoc:1701.332924

Arkiv for Matematik, 37, (2), 395-407, 1997.11
Let$M$be a connected, noncompact, complete Riemannian manifold, consider the operator$L=Δ+∇V$for some$V∈C$^{2}(M) with exp[$V$] integrable with respect to the Riemannian volume element. This paper studies the existence of the spectral gap of$L$. As a consequence of the main result, let ϱ be the distance function from a point o, then the spectral gap exists provided lim_{ϱ→∞}sup$L$_{ϱ<0}while the spectral gap does not exist if o is a pole and lim_{ϱ→∞}inf$L$_{ϱ≥0}. Moreover, the elliptic operators on$R$^{$d$}are also studied.
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@inproceedings{feng-yu1997existence,
  title={Existence of the spectral gap for elliptic operators},
  author={Feng-Yu Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203557003546733},
  booktitle={Arkiv for Matematik},
  volume={37},
  number={2},
  pages={395-407},
  year={1997},
}
Feng-Yu Wang. Existence of the spectral gap for elliptic operators. 1997. Vol. 37. In Arkiv for Matematik. pp.395-407. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203557003546733.
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