Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On the isoperimetric constant of symmetric spaces of noncompact type
HTML articles powered by AMS MathViewer

by Xiaodong Wang PDF
Proc. Amer. Math. Soc. 143 (2015), 4885-4891 Request permission

Abstract:

We prove that the isoperimetric constant is positive for all symmetric spaces of noncompact type and compute it explicitly.
References
  • G. Besson, G. Courtois, and S. Gallot, Volume et entropie minimale des espaces localement symétriques, Invent. Math. 103 (1991), no. 2, 417–445 (French). MR 1085114, DOI 10.1007/BF01239520
  • Isaac Chavel, Riemannian geometry, 2nd ed., Cambridge Studies in Advanced Mathematics, vol. 98, Cambridge University Press, Cambridge, 2006. A modern introduction. MR 2229062, DOI 10.1017/CBO9780511616822
  • Jeff Cheeger, A lower bound for the smallest eigenvalue of the Laplacian, Problems in analysis (Papers dedicated to Salomon Bochner, 1969) Princeton Univ. Press, Princeton, N. J., 1970, pp. 195–199. MR 0402831
  • Patrick B. Eberlein, Geometry of nonpositively curved manifolds, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1996. MR 1441541
  • Ernst Heintze and Hans-Christoph Im Hof, Geometry of horospheres, J. Differential Geometry 12 (1977), no. 4, 481–491 (1978). MR 512919
  • Sigurdur Helgason, Differential geometry, Lie groups, and symmetric spaces, Pure and Applied Mathematics, vol. 80, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 514561
  • F. I. Karpelevič, The geometry of geodesics and the eigenfunctions of the Beltrami-Laplace operator on symmetric spaces, Trans. Moscow Math. Soc. 1965 (1967), 51–199. Amer. Math. Soc., Providence, R.I., 1967. MR 0231321
  • S. Kobayashi and K. Nomizu, The Foundations of Differential Geometry, Addison Wesley, Mass.
  • Anthony Manning, Topological entropy for geodesic flows, Ann. of Math. (2) 110 (1979), no. 3, 567–573. MR 554385, DOI 10.2307/1971239
  • M. A. Olshanetski, Martin boundary of the Laplace Beltrami operator on symmetric spaces of nonpositive curvature, Math. Nauk. 1969. (Russian).
  • R. Schoen and S.-T. Yau, Lectures on differential geometry, Conference Proceedings and Lecture Notes in Geometry and Topology, I, International Press, Cambridge, MA, 1994. Lecture notes prepared by Wei Yue Ding, Kung Ching Chang [Gong Qing Zhang], Jia Qing Zhong and Yi Chao Xu; Translated from the Chinese by Ding and S. Y. Cheng; With a preface translated from the Chinese by Kaising Tso. MR 1333601
  • R. Spatzier, Dynamical properties of algebraic systems– a study in closed geodesics, Thesis, University of Warwick, 1983.
  • Shing Tung Yau, Isoperimetric constants and the first eigenvalue of a compact Riemannian manifold, Ann. Sci. École Norm. Sup. (4) 8 (1975), no. 4, 487–507. MR 397619
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 53C35, 58J50
  • Retrieve articles in all journals with MSC (2010): 53C35, 58J50
Additional Information
  • Xiaodong Wang
  • Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
  • Email: xwang@math.msu.edu
  • Received by editor(s): June 30, 2014
  • Received by editor(s) in revised form: July 29, 2014
  • Published electronically: April 29, 2015
  • Communicated by: Guofang Wei
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 4885-4891
  • MSC (2010): Primary 53C35; Secondary 58J50
  • DOI: https://doi.org/10.1090/proc/12601
  • MathSciNet review: 3391046