Journal of Differential Geometry

Comparison theorem for Kähler manifolds and positivity of spectrum

Peter Li and Jiaping Wang

Full-text: Open access

Abstract

The first part of this paper is devoted to proving a comparison theorem for Kähler manifolds with holomorphic bisectional curvature bounded from below. The model spaces being compared to are ℙℂm, ℙm, and ℙℍm. In particular, it follows that the bottom of the spectrum for the Laplacian is bounded from above by m2 for a complete, m-dimensional, Kähler manifold with holomorphic bisectional curvature bounded from below by −1. The second part of the paper is to show that if this upper bound is achieved and when m=2, then it must have at most four ends.

Article information

Source
J. Differential Geom., Volume 69, Number 1 (2005), 043-074.

Dates
First available in Project Euclid: 16 July 2005

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1121540339

Digital Object Identifier
doi:10.4310/jdg/1121540339

Mathematical Reviews number (MathSciNet)
MR2169582

Zentralblatt MATH identifier
1087.53067

Citation

Li, Peter; Wang, Jiaping. Comparison theorem for Kähler manifolds and positivity of spectrum. J. Differential Geom. 69 (2005), no. 1, 043--074. doi:10.4310/jdg/1121540339. https://projecteuclid.org/euclid.jdg/1121540339


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