A sharp estimate for the bottom of the spectrum of the Laplacian on Kähler manifolds

Details A sharp estimate for the bottom of the spectrum of the Laplacian on Kähler manifolds A sharp estimate for the bottom of the spectrum of the Laplacian on Kähler manifolds

2007-03-03

arxiv.org/abs/math/0703098v1

Mathematics

Differential Geometry

26 pages

Scientific paper

On a complete noncompact K\"{a}hler manifold we prove that the bottom of the spectrum for the Laplacian is bounded from above by $m^2$ if the Ricci curvature is bounded from below by $-2(m+1)$. Then we show that if this upper bound is achieved then the manifold has at most two ends. These results improve previous results on this subject proved by P. Li and J. Wang in \cite {L-W3} and \cite{L-W} under assumptions on the bisectional curvature.

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