@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},
year = {2000},
publisher = {Institut des Hautes Etudes Scientifiques},
volume = {92},
mrnumber = {1839486},
zbl = {1003.58007},
language = {en},
url = {https://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 Etudes Scientifiques UR - https://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 Etudes Scientifiques %U https://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, Tome 92 (2000), pp. 5-62. https://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. | Zbl | MR
[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. | Zbl | MR
[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. | Zbl | MR
[BT] , , Algebraic models defined over Q of differentiable manifolds, Geom. Dedicata, 42 (1992), 155-162. | Zbl | MR
[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. | Zbl | MR
[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. | Zbl | MR
[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. | Zbl | MR
[Baum] , Topics in combinatorial group theory, Boston, Birkhauser, 1993. | Zbl | MR
[BMR] , , , Smoothing Riemannian metrics, Math. Z., 188 (1984), 69-74. | Zbl | MR
[BP] , , Lectures on hyperbolic geometry, Springer, 1992. | Zbl | MR
[BN] , , Multidimensional generalized Riemannian spaces, in Geometry IV, ed. Yu. G. Reshetnyak, Encyclopaedia of Mathematical Sciences, vol. 70, Springer, 1993. | Zbl | MR
[Br] , Recent trends in Riemannian geometry, in Recent trends in mathematics, Reinhardsbrunn 1982, 20-37, Leipzig, Teubner, 1982. | Zbl
[Be] , Einstein manifolds, Springer, 1987. | Zbl | MR
[BW] , , Arithmetic manifolds with positive scalar curvature, preprint. | Zbl
[BCR] , , , Geometrie Algebrique Reelle, Springer, 1987. | Zbl | MR
[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. | Zbl | MR
[Bor 1] , Compact Clifford-Klein forms of symmetric spaces, Topology 2 (1963), 111-122. | Zbl | MR
[Bor 2] , Stable real cohomology of arithmetic groups, Ann. Sc. École Norm. Sup. 7 (1974), 235-272. | Zbl | MR | Numdam
[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. | Zbl | MR
[BorWal] , , Continuous cohomology, discrete subgroups and representations of reductive groups, Ann. of Math. Studies 94, Princeton Univ. Press, 1980. | Zbl | MR
[BY] , , The rank conjecture for number fields, Math. Res. Lett. 1 (1994), 689-699. | Zbl | MR
[Bou] , Une stratification de l'espace des structures riemanniennes, Comp. Math., 30 (1975), 1-41. | Zbl | MR | Numdam
[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. | Zbl | MR
[Ch] , Riemannian geometry: a modern introduction, Cambridge University Press, 1995. | Zbl
[C] , Finiteness theorems for Riemannian manifolds, Amer. J. Math. 92 (1970), 61-74. | Zbl | MR
[CMS] , , , On the curvature of piecewise-flat spaces, Comm. Math. Phys. 92 (1984), 405-454. | Zbl | MR
[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. | Zbl | MR
[C10] , Représentations galoisiennes associées aux représentations automorphes autoduales de GL(n), Publications IHES, 73 (1991), 97-145. | Zbl | MR | Numdam
[C1] , On the cohomology of Kottwitz's arithmetic varieties, Duke Math. J., 72 (1993), 757-795. | Zbl | MR
[CoSh] , , Nash triviality for families of Nash manifolds, Inv. Math. 108 (1992), 349-368. | Zbl | MR
[D] , Minimal-program complexity of sequences with restricted resources, Inf. and Control 23 (1973), 301-312. | Zbl | MR
[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. | Zbl | MR
[GM] , , Rational Homotopy Theory and Differential Forms, Birkhauser, 1981. | Zbl | MR
[Gr 1] , Volume and bounded cohomology, Publications IHES 56 (1982), 5-99. | Zbl | MR | Numdam
[Gr 2] , Filling of Riemannian manifolds, J. Differential Geom., 18 (1983), 1-148. | Zbl | MR
[GL 1] , , The classification of simply connected manifolds of positive scalar curvature, Ann. Math. 111 (1980), 209-230. | Zbl | MR
[GL 2] , , Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Publications IHES, 58 (1983), 295-408. | Zbl | MR | Numdam
[GP] , , Bounding homotopy type by geometry, Ann. Math. 128 (1988), 195-206. | Zbl | MR
[Ha] , Three-manifolds with positive Ricci curvature, J. Diff. Geometry 17 (1982), 255-306. | Zbl | MR
[Haus] , Manifolds with a given homology and fundamental group, Commun. Math. Helv. 53 (1978), 113-134. | Zbl | MR
[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. | Zbl | MR
[KS] , , The subgroups of a free product of two groups with an amalgamated subgroup, Trans. Amer. Math. Soc. 150 (1970), 227-255. | Zbl | MR
[KaS] , , Groups acting on buildings, operator K-theory, and Novikov's conjecture, K-theory, 4 (1991), 303-337. | Zbl | MR
[K0] , Smooth homology spheres and their fundamental groups, Trans. Amer. Math. Soc. 144 (1969), 67-72. | Zbl | MR
[K] , Multiplicateurs de Schur et K-theories, in Essays in topology and related topics, ed. A. Haefliger and R. Narashimhan, Springer, 1970, 212-225. | Zbl | MR
[Kt0] , Stable trace formula: cuspidal tempered terms, Duke Math. J. 51 (1984), 611-650. | Zbl | MR
[Kt1] , Stable trace formula: elliptic singular terms, Math. Ann. 275 (1986), 365-399. | Zbl | MR
[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. | Zbl | MR
[LS] , , Combinatorial group theory, Springer, 1977. | Zbl | MR
[LV] , , Kolmogorov complexity and its applications, in Handbook of theoretical computer science, ed. by Jan van Leeuwen, Elsevier, 1990, 187-254. | Zbl | MR
[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. | Zbl | MR
[Mil 1] , Introduction to algebraic K-theory, Annals of Mathematical Studies, Princeton Univ. Press, 1971. | Zbl | MR
[Mil 2] , On the homology of Lie groups made discrete, Comm. Math. Helv., 58 (1983), 72-85. | Zbl | MR
[N1] , Einstein structures: existence versus uniqueness, Geom. Funct. Anal. 5 (1995), 76-91. | Zbl | MR
[N2] , Geometry of the space of triangulations of a compact manifold, Commun. Math. Phys., 181 (1996), 303-330. | Zbl | MR
[N3] , Disconnectedness of sublevel sets of some Riemannian functionals, Geom. Funct. Anal. 6 (1996), 703-725. | Zbl | MR
[N4] , Fundamental group and contractible closed geodesics, Comm. on Pure and Appl. Math. 49 (12) (1996), 1257-1270. | Zbl | MR
[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. | Zbl | MR
[Pi1] , KK-groups of crossed products by groups acting on trees, Invent. Math., 86 (1986), 603-634. | Zbl | MR
[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. | Zbl | MR
[Ros 1] , C*-algebras, positive scalar curvature, and the Novikov conjecture, Publications IHES, 58 (1983), 197-212. | Zbl | MR | Numdam
[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. | Zbl | MR
[Ser] , Arithmetic groups, in Homological group theory, ed. by C. T. C. Wall, 105-136, Cambridge, Cambridge Univ. Press, 1979. | Zbl | MR
[Sch] , Variational theory for the total scalar curvature functional for Riemannian metrics and related topics, Springer, LNM 1365 (1989), 120-154. | Zbl | MR
[S] , Infinitesimal computations in topology, Publications IHES 47 (1977), 269-331. | Zbl | MR | Numdam
[T] , Thin position and the recognition problem for S3, Math. Res. Lett. 1 (1994), 613-630. | Zbl | MR
[V] , Un théorème d'Hurewicz homologique, Commun. Math. Helv. 52 (1977), 393-413. | Zbl | MR
[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. | Zbl | MR
[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. | Zbl | MR






