Journal of Differential Geometry

Complete Manifolds with Positive Spectrum

Peter Li and Jiaping Wang


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.

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

First available in Project Euclid: 20 July 2004

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

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