Analytic inequalities, and rough isometries between non-compact Riemannian manifolds

P. Buser, A note on the isoperimetric constant, Ann. Sci. École Norm. Sup. 15 (1982), 213–230.
MathSciNet MATH Google Scholar
J. Cheeger, A lower bound for the smallest eigenvalue of the laplacian, in “Rroblems in Analysis (A symposium in Honor of S. Bochner)”, Princeton Univ. Press, Princeton, 1970, pp. 195–199.
Google Scholar
C.B. Croke, Some isoperimetric inequalities and eigenvalue estimates, Ann. Sci. École Norm. Sup. 13 (1980), 419–435.
MathSciNet MATH Google Scholar
H. Federer and W. H. Fleming, Normal and integral currents, Ann. of Math. 72 (1960), 458–520.
Article MathSciNet MATH Google Scholar
M. Kanai, Rough isometries, and combinatorial approximations of geometries of non-compact riemannian manifolds, J. Math. Soc. Japan 37 (1985), 391–413.
Article MathSciNet MATH Google Scholar
_____, Rough isometries and the parabolicity of riemannian manifolds.
Google Scholar
_____, Rough isometries and isoperimetic inequalities for non-compact riemannian manifolds, to appear in the proceedings of “The 6th Symposium on Differential Equations and Differential Geometry”, held at Fudan Univ., Shanghai, 1985.
Google Scholar
H. Kesten, Symmetric random walks on groups, Trans. Amer. Math. Soc. 92 (1959), 336–354.
Article MathSciNet MATH Google Scholar
_____, Full Banach mean values on countable groups, Math. Scand. 7 (1959), 146–156.
MathSciNet MATH Google Scholar
V. G. Maz'ya, Classes of domains and imbedding theorems for function spaces, Dokl. Akad. Nauk SSSR 133 (1960), 527–530; English transl., Soviet Math. Dokl. 1 (1960), 882–885.
MathSciNet MATH Google Scholar
R. Osserman, The isoperimetric inequality, Bull. Amer. Math. Soc. 84 (1978), 1182–1238.
Article MathSciNet MATH Google Scholar
S.-T. Yau, Isoperimetric constants and the first eigenvalue of a compact riemannian manifold, Ann. Sci. École Norm. Sup. 8 (1975), 487–507.
MathSciNet MATH Google Scholar

Download references

Author information

Authors and Affiliations

Department of Mathematics Faculty of Science and Technology, Keio University, 223, Yokohama, Japan
Masahiko Kanai

Authors

Masahiko Kanai
View author publications
You can also search for this author in PubMed Google Scholar

Editor information

Katsuhiro Shiohama Takashi Sakai Toshikazu Sunada

Rights and permissions

Reprints and permissions

Copyright information

About this paper

Cite this paper

Kanai, M. (1986). Analytic inequalities, and rough isometries between non-compact Riemannian manifolds. In: Shiohama, K., Sakai, T., Sunada, T. (eds) Curvature and Topology of Riemannian Manifolds. Lecture Notes in Mathematics, vol 1201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075650

Download citation

DOI: https://doi.org/10.1007/BFb0075650
Published: 16 September 2006
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16770-9
Online ISBN: 978-3-540-38827-2
eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Analytic inequalities, and rough isometries between non-compact Riemannian manifolds

Access this chapter

Preview

References