@article{PMIHES_2000__92__5_0, author = {Nabutovsky, Alexander and Weinberger, Shmuel}, title = {Variational problems for riemannian functionals and arithmetic groups}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {5--62}, publisher = {Institut des Hautes \'Etudes Scientifiques}, volume = {92}, year = {2000}, mrnumber = {1839486}, zbl = {1003.58007}, language = {en}, url = {http://www.numdam.org/item/PMIHES_2000__92__5_0/} }
TY - JOUR AU - Nabutovsky, Alexander AU - Weinberger, Shmuel TI - Variational problems for riemannian functionals and arithmetic groups JO - Publications Mathématiques de l'IHÉS PY - 2000 SP - 5 EP - 62 VL - 92 PB - Institut des Hautes Études Scientifiques UR - http://www.numdam.org/item/PMIHES_2000__92__5_0/ LA - en ID - PMIHES_2000__92__5_0 ER -
%0 Journal Article %A Nabutovsky, Alexander %A Weinberger, Shmuel %T Variational problems for riemannian functionals and arithmetic groups %J Publications Mathématiques de l'IHÉS %D 2000 %P 5-62 %V 92 %I Institut des Hautes Études Scientifiques %U http://www.numdam.org/item/PMIHES_2000__92__5_0/ %G en %F PMIHES_2000__92__5_0
Nabutovsky, Alexander; Weinberger, Shmuel. Variational problems for riemannian functionals and arithmetic groups. Publications Mathématiques de l'IHÉS, Volume 92 (2000), pp. 5-62. http://www.numdam.org/item/PMIHES_2000__92__5_0/
[AVS] Geometry of spaces of constant curvature, in Geometry II, ed. by E. Vinberg, Encyclopaedia of Math. Sci., vol. 29, Springer, 1993. | MR | Zbl
, , ,[An 1] Degeneration of metrics with bounded curvature and applications to critical metrics of Riemannian functionals, in Differential Geometry: Riemannian Geometry, Proceedings of symposia in pure mathematics, ed. by R. Greene and S. T. Yau, 54:3 (1993), 53-79. | MR | Zbl
,[An 2] Scalar curvature and geometrization conjectures for 3-manifolds, in Comparison Geometry, ed. by K. Grove and P. Petersen, 49-82, MSRI Publications, 1997. | MR | Zbl
,[BT] Algebraic models defined over Q of differentiable manifolds, Geom. Dedicata, 42 (1992), 155-162. | MR | Zbl
, ,[BGS] Manifolds of non-positive sectional curvature, Birkhauser, Boston, 1985.
, , ,[Ba] Real Analyticity of solutions of Hamilton's equation, Math. Z., 195 (1987), 93-97. | MR | Zbl
,[B] Complexity of programs to determine whether natural numbers not greater than n belong to a recursively enumerable set, Soviet Math. Dokl. 9 (1968), 1251-1254. | Zbl
,[BC] Chern character for discrete groups, in A fête of topology, 163-232, Academic Press, 1988. | MR | Zbl
, ,[BCH] Classifying space for proper actions and K-theory of group C*-algebras, in C*-algebras: 1943-1993 (San Antonio, TX, 1993), 240-291, Contemp. Math., 167, Amer. Math. Soc., Providence, RI, 1994. | MR | Zbl
, , ,[Baum] Topics in combinatorial group theory, Boston, Birkhauser, 1993. | MR | Zbl
,[BMR] Smoothing Riemannian metrics, Math. Z., 188 (1984), 69-74. | MR | Zbl
, , ,[BP] Lectures on hyperbolic geometry, Springer, 1992. | MR | Zbl
, ,[BN] Multidimensional generalized Riemannian spaces, in Geometry IV, ed. Yu. G. Reshetnyak, Encyclopaedia of Mathematical Sciences, vol. 70, Springer, 1993. | MR | Zbl
, ,[Br] Recent trends in Riemannian geometry, in Recent trends in mathematics, Reinhardsbrunn 1982, 20-37, Leipzig, Teubner, 1982. | Zbl
,[Be] Einstein manifolds, Springer, 1987. | MR | Zbl
,[BW] Arithmetic manifolds with positive scalar curvature, preprint. | Zbl
, ,[BCR] Geometrie Algebrique Reelle, Springer, 1987. | MR | Zbl
, , ,[BHP] On recursively unsolvable problems in topology and their classification, in Contributions to mathematical logic (H. Arnold Schmidt, K. Schutte, H.-J. Thiele, eds.), North-Holland, 1968. | MR | Zbl
, , ,[Bor 1] Compact Clifford-Klein forms of symmetric spaces, Topology 2 (1963), 111-122. | MR | Zbl
,[Bor 2] Stable real cohomology of arithmetic groups, Ann. Sc. École Norm. Sup. 7 (1974), 235-272. | Numdam | MR | Zbl
,[Bor 3] Stable real cohomology of arithmetic groups II, in Manifolds and Lie groups, ed. by J. Hano et al., 21-56, Boston, Birkhauser, 1981. | MR | Zbl
,[BorWal] Continuous cohomology, discrete subgroups and representations of reductive groups, Ann. of Math. Studies 94, Princeton Univ. Press, 1980. | MR | Zbl
, ,[BY] The rank conjecture for number fields, Math. Res. Lett. 1 (1994), 689-699. | MR | Zbl
, ,[Bou] Une stratification de l'espace des structures riemanniennes, Comp. Math., 30 (1975), 1-41. | Numdam | MR | Zbl
,[BGP] A. D. Alexandrov spaces with curvature bounded from below, Russ. Math. Surv. 47 (1992), 1-58. | Zbl
, , ,[CS] The codimension two placement problem and the homology equivalent manifolds, Ann. Math. 99 (1974), 277-348. | MR | Zbl
, ,[Ch] Riemannian geometry: a modern introduction, Cambridge University Press, 1995. | Zbl
,[C] Finiteness theorems for Riemannian manifolds, Amer. J. Math. 92 (1970), 61-74. | MR | Zbl
,[CMS] On the curvature of piecewise-flat spaces, Comm. Math. Phys. 92 (1984), 405-454. | MR | Zbl
, , ,[CGT] Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Diff. Geom. 17 (1982), 15-53. | MR | Zbl
, , ,[C10] Représentations galoisiennes associées aux représentations automorphes autoduales de GL(n), Publications IHES, 73 (1991), 97-145. | Numdam | MR | Zbl
,[C1] On the cohomology of Kottwitz's arithmetic varieties, Duke Math. J., 72 (1993), 757-795. | MR | Zbl
,[CoSh] Nash triviality for families of Nash manifolds, Inv. Math. 108 (1992), 349-368. | MR | Zbl
, ,[D] Minimal-program complexity of sequences with restricted resources, Inf. and Control 23 (1973), 301-312. | MR | Zbl
,[FHT] Rational Homotopy Theory, to appear. | Zbl
, , ,[F] Hausdorff convergence of Riemannian manifolds and its applications, in Recent Topics in Differential and Analytic Geometry, ed. T. Ochiai, Adv. Stud. Pure Math. 18-I, Boston, Academic Press, 1990. | MR | Zbl
,[GM] Rational Homotopy Theory and Differential Forms, Birkhauser, 1981. | MR | Zbl
, ,[Gr 1] Volume and bounded cohomology, Publications IHES 56 (1982), 5-99. | Numdam | MR | Zbl
,[Gr 2] Filling of Riemannian manifolds, J. Differential Geom., 18 (1983), 1-148. | MR | Zbl
,[GL 1] The classification of simply connected manifolds of positive scalar curvature, Ann. Math. 111 (1980), 209-230. | MR | Zbl
, ,[GL 2] Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Publications IHES, 58 (1983), 295-408. | Numdam | MR | Zbl
, ,[GP] Bounding homotopy type by geometry, Ann. Math. 128 (1988), 195-206. | MR | Zbl
, ,[Ha] Three-manifolds with positive Ricci curvature, J. Diff. Geometry 17 (1982), 255-306. | MR | Zbl
,[Haus] Manifolds with a given homology and fundamental group, Commun. Math. Helv. 53 (1978), 113-134. | MR | Zbl
,[H] Differential geometry, Lie groups, and symmetric spaces, New York, Academic Press, 1978. | Zbl
,[I] Foundations of the theory of bounded cohomology, J. of Soviet Math., 37 (1987), 1090-1115. | Zbl
,[JK] Geometrische Methoden zur Gewinnung von A-Priori-Schranken fur harmonische Abbildungen, Manuscripta Math., 40 (1982), 27-78. | MR | Zbl
, ,[KS] The subgroups of a free product of two groups with an amalgamated subgroup, Trans. Amer. Math. Soc. 150 (1970), 227-255. | MR | Zbl
, ,[KaS] Groups acting on buildings, operator K-theory, and Novikov's conjecture, K-theory, 4 (1991), 303-337. | MR | Zbl
, ,[K0] Smooth homology spheres and their fundamental groups, Trans. Amer. Math. Soc. 144 (1969), 67-72. | MR | Zbl
,[K] Multiplicateurs de Schur et K-theories, in Essays in topology and related topics, ed. A. Haefliger and R. Narashimhan, Springer, 1970, 212-225. | MR | Zbl
,[Kt0] Stable trace formula: cuspidal tempered terms, Duke Math. J. 51 (1984), 611-650. | MR | Zbl
,[Kt1] Stable trace formula: elliptic singular terms, Math. Ann. 275 (1986), 365-399. | MR | Zbl
,[L] Global and local curvatures, in Riemannian Geometry, ed. by M. Lovric, M. Min-Oo, M. Wang, Fields Institute Monograph, 4, American Mathematical Society, 1996, 23-52. | MR | Zbl
,[LS] Combinatorial group theory, Springer, 1977. | MR | Zbl
, ,[LV] Kolmogorov complexity and its applications, in Handbook of theoretical computer science, ed. by Jan van Leeuwen, Elsevier, 1990, 187-254. | MR | Zbl
, ,[Ma] Arithmetic groups, Springer, 1991.
,[M] Decision problems for groups-survey and reflections, in Combinatorial group theory (G. Baumslag, C. Miller, eds.), Springer 1989, 1-59. | MR | Zbl
,[Mil 1] Introduction to algebraic K-theory, Annals of Mathematical Studies, Princeton Univ. Press, 1971. | MR | Zbl
,[Mil 2] On the homology of Lie groups made discrete, Comm. Math. Helv., 58 (1983), 72-85. | MR | Zbl
,[N1] Einstein structures: existence versus uniqueness, Geom. Funct. Anal. 5 (1995), 76-91. | MR | Zbl
,[N2] Geometry of the space of triangulations of a compact manifold, Commun. Math. Phys., 181 (1996), 303-330. | MR | Zbl
,[N3] Disconnectedness of sublevel sets of some Riemannian functionals, Geom. Funct. Anal. 6 (1996), 703-725. | MR | Zbl
,[N4] Fundamental group and contractible closed geodesics, Comm. on Pure and Appl. Math. 49 (12) (1996), 1257-1270. | MR | Zbl
,[P] Gromov-Hausdorff convergence of metric spaces, in Differential Geometry: Riemannian Geometry, ed. by R. Greene, S. T. Yau, Proceedings of AMS Symposia in Pure Mathematics, 54:3 (1993), 489-504. | MR | Zbl
,[Pi1] KK-groups of crossed products by groups acting on trees, Invent. Math., 86 (1986), 603-634. | MR | Zbl
,[Pi2] K-theory for groups acting on trees, Proceedings of the Int. Congr. of Math., Kyoto, 1990, 979-986, Math. Soc. Japan, 1991. | Zbl
,[R] An introduction to the theory of groups, Springer, 1995. | MR | Zbl
,[Ros 1] C*-algebras, positive scalar curvature, and the Novikov conjecture, Publications IHES, 58 (1983), 197-212. | Numdam | MR | Zbl
,[Ros 2] Algebraic K-theory and its applications, Springer, 1993.
,[Sr] Extremal geometries, in Extremal Riemann surfaces, ed. by J. R. Quine and Peter Sarnak, Contemp. Math. 201, 1-7, AMS, Providence, RI, 1997. | MR | Zbl
,[Ser] Arithmetic groups, in Homological group theory, ed. by C. T. C. Wall, 105-136, Cambridge, Cambridge Univ. Press, 1979. | MR | Zbl
,[Sch] Variational theory for the total scalar curvature functional for Riemannian metrics and related topics, Springer, LNM 1365 (1989), 120-154. | MR | Zbl
,[S] Infinitesimal computations in topology, Publications IHES 47 (1977), 269-331. | Numdam | MR | Zbl
,[T] Thin position and the recognition problem for S3, Math. Res. Lett. 1 (1994), 613-630. | MR | Zbl
,[V] Un théorème d'Hurewicz homologique, Commun. Math. Helv. 52 (1977), 393-413. | MR | Zbl
,[ZL] The complexity of finite objects and the development of the concepts of information and randomness by means of the theory of algorithms, Russ. Math. Surv. 25 (6) (1970), 83-129. | MR | Zbl
, ,[Y] Open problems in geometry, in Differential Geometry: Riemannian Geometry, ed. by R. Greene and S. T. Yau, Proceedings of AMS Symposia in Pure Mathematics, 54:1 (1993), 1-28. | MR | Zbl
,