Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. P. Anker, L. Ji, Sharp bounds on the heat kernel and Green function estimates on noncompact symmetric spaces, GAFA 9 (1999), 1035–1091.
A. Ancona, Negatively curved manifolds, elliptic operators, and the Martin boundary, Ann. of Math. 125 (1987), 495–536.
M. Anderson, R. Schoen, Positive harmonic functions on complete manifolds of negative curvature, Ann. of Math. 121 (1985), 429–461.
A. Ash, D. Mumford, M. Rapaport, Y. Tai, Smooth compactifications of locally symmetric varieties, Math Sci Press, Brookline, Mass, 1975.
W. L. Baily, A. Borel, Compactification of arithmetic quotients of bounded symmetric domains, Ann. of Math. 84 (1966), 442–528.
W. Ballmann, M. Gromov, V. Schroeder, Manifolds of nonpositive curvature, Progress in Math., Vol. 61, Birkhäuser, Boston, 1985.
A. Borel, Introduction aux groupes arithmétiques, Hermann, Paris, 1969.
A. Borel, Semisimple Groups and Riemannian Symmetric Spaces, Texts & Readings in Math. Vol. 16, Hindustan Book Agency, New Delhi, 1998.
A. Borel, L. Ji, Compactifications of locally symmetric spaces, to appear in J. Diff. Geom.
A. Borel, L. Ji, Compactifications of symmetric spaces, to appear in J. Diff. Geom.
A. Borel, L. Ji, Compactifications of symmetric and locally symmetric spaces, Math. Research Letters 9 (2002), 725–739.
A. Borel, L. Ji, Compactifications of Symmetric and Locally Symmetric Spaces, in this volume.
A. Borel, J. P. Serre, Corners and Arithmetic Groups, Comment. Math. Helv. 48 (1973), 436–491.
N. Bourbaki, Éléments de Mathématique, Livre VI, Intégration, Hermann, Paris, 1963.
K. Brown, Buildings, Springer-Verlag, New York, 1989.
K. Burns, R. Spatzier, On the topological Tits buildings and their classifications, IHES 65 (1987), 5–34.
J. Cheeger, D. Ebin, Comparison Theorems in Riemannian Geometry, North-Holland Publishing Co., 1975.
H. Furstenberg, A Poisson formula for semi-simple Lie groups, Ann. of Math. 72 (1963), 335–386.
Y. Guivarc’h, L. Ji, J. C. Taylor, Compactifications of Symmetric Spaces, Progress in Math., Vol. 156, Birkhäuser, Boston, 1998.
Y. Guivarc’h, J. C. Taylor, The Martin compactification of the polydisc at the bottom of the positive spectrum, Colloquium Math LX/LXI (1990), 537–546.
S. Giulini, W. Woess, The Martin compactification of the cartesian product of two hyperbolic spaces, J. für die Reine u. angew. Math., 444 (1993), 17–28.
S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York, 1978.
L. Ji, Satake and Martin compactifications of symmetric spaces are topological balls, Math. Res Letters, 4 (1997), 79–89.
L. Ji, The greatest common quotient of Borel-Serre and the Toroidal Compactifications, Geometric and Functional Analysis, 8 (1998), 978–1015.
L. Ji, R. MacPherson, Geometry of compactifications of locally symmetric spaces, Ann. Inst. Fourier, 52 (2002), 457–559.
F. I. Karpelevic, The geometry of geodesics and the eigenfunctions of the Beltrami-Laplace operator on symmetric spaces, Trans. Moscow Math. Soc., 14 (1965), 51–199.
M. P. Malliavin, P. Malliavin, Factorisation et lois limites de la diffusion horizontale audessus d’un espace Riemannien symétrique, Lecture Notes in Math., Vol. 404, 1974, Springer-Verlag.
R. S. Martin, Minimal positive harmonic functions, Trans. Amer. Math. Soc., 49 (1941), 137–172.
C. C. Moore, Compactifications of symmetric spaces I, Amer. J. Math., 86 (1964), 201–218.
T. Oshima, A realization of Riemannian symmetric spaces, J. Math. Soc. Japan, 30 (1978), 117–132.
T. Oshima, A realization of semisimple symmetric spaces and construction of boundary value maps, in Adv. Studies in Pure Math. Vol. 14, Representations of Lie groups, 1986, pp. 603–650.
T. Oshima, J. Sekiguchi, Eigenspaces of invariant differential operators on an affine symmetric spaces, Invent. Math., 57 (1980), 1–81.
I. Satake, On representations and compactifications of symmetric spaces, Ann. of Math. 71 (1960), 77–110.
I. Satake, On compactifications of the quotient spaces for arithmetically defined discontinuous groups, Ann. of Math. 72 (1960), 555–580.
D. Sullivan, Related aspects of positivity in Riemannian geometry, J. Diff. Geom., 25 (1987), 327–308.
J. C. Taylor, The Martin compactification of a symmetric space of non-compact type at the bottom of the positive spectrum: An introduction, in Potential Theory, M. Kishi, ed. Walter de Gruyter & Co., Berlin, 1991, pp. 127–139.
J. C. Taylor, Martin compactification, in Topics in Probability and Lie groups: Boundary Theory, J. C. Taylor, ed., in CRM-AMS, 2001, pp. 153–202.
S. Zucker, L2 cohomology of warped products and arithmetic groups, Invent. Math., 70 (1982), 169–218.
S. Zucker, Satake compactifications, Comment. Math. Helv. 58 (1983), 312–343.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Birkhäuser Boston
About this chapter
Cite this chapter
Ji, L. (2005). Introduction to Symmetric Spaces and Their Compactifications. In: Anker, JP., Orsted, B. (eds) Lie Theory. Progress in Mathematics, vol 229. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4430-X_1
Download citation
DOI: https://doi.org/10.1007/0-8176-4430-X_1
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-3526-8
Online ISBN: 978-0-8176-4430-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)