On the spectrum of a finite-volume negatively-curved manifold

American Journal of Mathematics

Volumn 123, Issue 2, 2001, Pages 185-205

  Lott, John ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035315395     PISSN: 00029327     EISSN: None     Source Type: Journal    
DOI: 10.1353/ajm.2001.0012     Document Type: Article

References (14)

1. J. Cheeger, K. Fukaya and M. Gromov, Nilpotent structures and invariant metrics on collapsed manifolds, J. Amer. Math. Soc. 5 (1992), 327-372.
2. J. Dodziuk, Eigenvalues of the Laplacian on Forms, Proc. Amer. Math. Soc. 85 (1982), 437-443.
3. H. Donnelly and P. Li, Pure point spectrum and negative curvature for noncompact manifolds, Duke Math. J. 46 (1979), 497-503.
4. H. Donnelly and F. Xavier, On the differential form spectrum of negatively curved Riemannian manifolds, Amer. J. Math. 106 (1984), 169-185.
5. N. Dunford and J. Schwartz, Linear Operators, Interscience Publishers, New York, 1963.
6. P. Eberlein, Lattices in spaces of nonpositive curvature, Ann. of Math. 111 (1980), 435-476.
7. E. Heintze and H.-C. Im Hof, Geometry of horospheres, J. Differential Geom. 12 (1977), 481-491.
8. J. Lott, The zero-in-the-specirum question, Enseign. Math. 42 (1996), 341-376.
9. 2-cohomology of geometrically infinite hyperbolic 3-manifolds, Geom. Funct. Anal. 7 (1997), 81-119.
10. _, Collapsing and the differential form laplacian, preprint, 1999, http://www.math.lsa.umich.edu/~lott.
11. W. Müller, Manifolds with Cusps of Rank One, Lecture Notes in Math., vol. 1244, Springer-Verlag, New York, 1987.
12. M. Reed and B. Simon, Methods in Mathematical Physics, Academic Press, New York, 1978.
13. Z. Shen, On complete manifolds of nonnegative kth-Ricci curvature, Trans. Amer. Math. Soc. 338 (1993), 289-310.
14. _, On complete Riemannian manifolds with collapsed ends, Pacific J. Math. 163 (1994), 175-182.