The fundamental group and the spectrum of the laplacian

Robert Brooks1
1Dept of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, USA

Tóm tắt

Từ khóa


Tài liệu tham khảo

W. K. Allard,On the First Variation of a Varifold, Ann. Math.95 (1972), 417–491.

R. Brooks,Exponential Growth and the Spectrum of the Laplacian, Proc. AMS82 (1981), 473–477.

—,Some Remarks on Bounded Cohomology, Ann. Math. Studies97 (1980), 53–63.

J. Cheeger,A Lower Bound for the Smallest Eigenvalue of the Laplacian, in Gunning,Problems in Analysis (1970), 195–199.

J. Cheeger andS. T. Yau,A Lower Bound for the Heat Kernel, preprint.

S. Y. Cheng andS. T. Yau,Differential Equations on Riemannian Manifolds and their Geometric Applications, Comm. Pure and Appl. Math.,28 (1975), 333–354.

H. Donnelly,Asymptotic Expansions for the Compact Quotients of Properly Discontinuous Group Actions, Ill. J. of Math.23 (1979), 485–496.

P. Eberlein,Some Properties of the Fundamental Group of a Fuchsian Manifold, Inventiones Math.19 (1973), 5–13.

F. Eisenberg, Ph.D. thesis, Stony Brook (1979).

F. P. Greenleaf,Invariants Means on Topological Groups and their Applications, von Nostrand, Reinhold & Co., 1969.

M. Hirsch andW. Thurston,Foliated Bundles, Invariant Measures, and Flat Manifolds, Ann. Math.101 (1975), 369–390.

H. Kesten,Full Banach Mean Values on Countable Groups, Math. Scand.7 (1959), 146–156.

H. P. McKean,An Upper Bound to the Spectrum of Δ on a Manifold of Negative Curvature, J. Diff. Geometry4 (1970), 359–366.

J. Milnor,A Note on Curvature and Fundamental Group, J. Diff. Geom.2 (1968), 1–7.

J. Tits,Free Subgroups in Linear Groups, J. Algebra20 (1972), 250–270.

H. Federer,Geometric Measure Theory, Springer Verlag (1969).

E. Følner,On groups with Full Banach Mean Value, Math. Scand.3 (1955), 243–254.

H. B. Lawson,Minimal Varieties in Real and Complex Geometry, Séminaire de Mathématiques Superieures, vol. 57, Université de Montréal, 1974.

S. T. Yau,Isoperimetric Constants and the First Eigenvalue of a Compact Riemannian Manifold, Ann. Sci. Éc. Norm. Sup. (1975) 487–507.