Journal of Differential Geometry

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

Ovidiu Munteanu

Full-text: Open access

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.

Article information

Source
J. Differential Geom., Volume 83, Number 1 (2009), 163-187.

Dates
First available in Project Euclid: 24 September 2009

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1253804354

Digital Object Identifier
doi:10.4310/jdg/1253804354

Mathematical Reviews number (MathSciNet)
MR2545033

Zentralblatt MATH identifier
1183.53068

Citation

Munteanu, Ovidiu. A sharp estimate for the bottom of the spectrum of the Laplacian on Kähler manifolds. J. Differential Geom. 83 (2009), no. 1, 163--187. doi:10.4310/jdg/1253804354. https://projecteuclid.org/euclid.jdg/1253804354


Export citation