Open Access
September 2009 A sharp estimate for the bottom of the spectrum of the Laplacian on Kähler manifolds
Ovidiu Munteanu
J. Differential Geom. 83(1): 163-187 (September 2009). DOI: 10.4310/jdg/1253804354
Abstract

On a complete noncompact Kähler 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.

Munteanu: A sharp estimate for the bottom of the spectrum of the Laplacian on Kähler manifolds
Copyright © 2009 Lehigh University
Ovidiu Munteanu "A sharp estimate for the bottom of the spectrum of the Laplacian on Kähler manifolds," Journal of Differential Geometry 83(1), 163-187, (September 2009). https://doi.org/10.4310/jdg/1253804354
Published: September 2009
Vol.83 • No. 1 • September 2009
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