Journal of Differential Geometry

Complete Manifolds with Positive Spectrum

Peter Li and Jiaping Wang

Abstract

In this paper, we studied complete manifolds whose spectrum of the Laplacian has a positive lower bound. In particular, if the Ricci curvature is bounded from below by some negative multiple of the lower bound of the spectrum, then we established a splitting type theorem. Moreover, if this assumption on the Ricci curvature is only valid outside a compact subset, then the manifold must have only finitely many ends with infinite volume. Similar type theorems are also obtained for complete Kähler manifolds.

Article information

Source
J. Differential Geom., Volume 58, Number 3 (2001), 501-534.

Dates
First available in Project Euclid: 20 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1090348357

Digital Object Identifier
doi:10.4310/jdg/1090348357

Mathematical Reviews number (MathSciNet)
MR1906784

Zentralblatt MATH identifier
1032.58016

Citation

Li, Peter; Wang, Jiaping. Complete Manifolds with Positive Spectrum. J. Differential Geom. 58 (2001), no. 3, 501--534. doi:10.4310/jdg/1090348357. https://projecteuclid.org/euclid.jdg/1090348357


Export citation