Harmonic maps into singular spaces and p-adic superrigidity for lattices in groups of rank one
Publications Mathématiques de l'IHÉS, Volume 76 (1992), pp. 165-246.
     author = {Gromov, Michael and Schoen, Richard},
     title = {Harmonic maps into singular spaces and $p$-adic superrigidity for lattices in groups of rank one},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {165--246},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {76},
     year = {1992},
     zbl = {0896.58024},
     mrnumber = {94e:58032},
     language = {en},
     url = {http://archive.numdam.org/item/PMIHES_1992__76__165_0/}
AU  - Gromov, Michael
AU  - Schoen, Richard
TI  - Harmonic maps into singular spaces and $p$-adic superrigidity for lattices in groups of rank one
JO  - Publications Mathématiques de l'IHÉS
PY  - 1992
DA  - 1992///
SP  - 165
EP  - 246
VL  - 76
PB  - Institut des Hautes Études Scientifiques
UR  - http://archive.numdam.org/item/PMIHES_1992__76__165_0/
UR  - https://zbmath.org/?q=an%3A0896.58024
UR  - https://www.ams.org/mathscinet-getitem?mr=94e:58032
LA  - en
ID  - PMIHES_1992__76__165_0
ER  - 
%0 Journal Article
%A Gromov, Michael
%A Schoen, Richard
%T Harmonic maps into singular spaces and $p$-adic superrigidity for lattices in groups of rank one
%J Publications Mathématiques de l'IHÉS
%D 1992
%P 165-246
%V 76
%I Institut des Hautes Études Scientifiques
%G en
%F PMIHES_1992__76__165_0
Gromov, Michael; Schoen, Richard. Harmonic maps into singular spaces and $p$-adic superrigidity for lattices in groups of rank one. Publications Mathématiques de l'IHÉS, Volume 76 (1992), pp. 165-246. http://archive.numdam.org/item/PMIHES_1992__76__165_0/

[ABB] S. B. Alexander, I. D. Berg and R. L. Bishop, The Riemannian obstacle problem, III. J. Math. 31 (1987), 167-184. | MR | Zbl

[Ag] S. Agmon, Unicité et convexité dans les problèmes différentiels, Sém. d'Analyse Sup., Univ. de Montréal, 1965. | Zbl

[Al] F. J. Almgren, Jr., Q-valued functions minimizing Dirichlet's integral and the regularity of area minimizing rectifiable currents up to codimension two, preprint, Princeton University.

[B] K. Brown, Buildings, Springer, New York, 1989. | MR | Zbl

[BT] F. Bruhat and J. Tits, Groupes réductifs sur un corps local. I. Données radicielles valuées, Publ. Math. IHES 41 (1972), 5-251. | Numdam | MR | Zbl

[C] K. Corlette, Archimedian superrigidity and hyperbolic geometry, Annals of Math., to appear. | Zbl

[Ch] Y. J. Chiang, Harmonic maps of V-manifolds, Ann. Global Anal. Geom. 8 (1990), 315-344. | MR | Zbl

[DM] P. Deligne and G. D. Mostow, Monodromy of hypergeometric functions and non-lattice integral monodromy, Publ. Math. IHES 63 (1986), 5-89. | Numdam | MR | Zbl

[ES] J. Eells and J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 109-160. | MR | Zbl

[F1] H. Federer, Geometric Measure Theory, Springer-Verlag, New York, 1969. | MR | Zbl

[F2] H. Federer, The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension, Bull. Amer. Math. Soc. 79 (1970), 761-771. | MR | Zbl

[G] H. Garland, P-adic curvature and the cohomology of discrete subgroups, Ann. of Math. 97 (1973), 375-423. | MR | Zbl

[GL] N. Garofalo and F. H. Lin, Monotonicity properties of variational integrals, Ap weights and unique continuation, Indiana Math. J. 35 (1986), 245-268. | MR | Zbl

[GP] M. Gromov, P, Pansu, Rigidity of lattices: An introduction, to appear in Springer Lecture Notes.

[GPS] M. Gromov and I. Piatetski-Shapiro, Non-arithmetic groups in Lobachevsky spaces, Publ. Math. IHES 66 (1988), 93-103. | Numdam | MR | Zbl

[GR] H. Garland and M. S. Raghunathan, Fundamental domains for lattices in R-rank 1 groups, Ann. of Math. 92 (1970), 279-326. | MR | Zbl

[Gro] M. Gromov, Partial differential relations, Springer Verlag, 1986. | MR | Zbl

[Ham] R. Hamilton, Harmonic maps of manifolds with boundary, Lecture Notes 471, Springer 1975. | MR | Zbl

[Har] P. Hartman, On homotopic harmonic maps, Can. J. Math. 19 (1967), 673-687. | MR | Zbl

[HV] P. De La Harpe and A. Valette, La propriété (T) de Kazhdan pour les groupes localement compacts, Astérisque 175 (1989), Soc. Math. de France. | Zbl

[K] H. Karcher, Riemannian center of mass and mollifier smoothing, Comm. Pure and Appl. Math. 30 (1977), 509-541. | MR | Zbl

[La1] E. M. Landis, A three-sphere theorem, Dokl. Akad. Nauk S.S.S.R. 148 (1963), 277-279. Translated in Soviet Math. 4 (1963), 76-78. | MR | Zbl

[La2] E. M. Landis, Some problems on the qualitative theory of second order elliptic equations (case of several variables), Uspekhi Mat. Nauk. 18 (1963), 3-62. Translated in Russian Math. Surveys 18 (1963), 1-62. | Zbl

[L] M. L. Leite, Harmonic mappings of surfaces with respect to degenerate metrics, Amer. J. Math. 110 (1988), 399-412. | MR | Zbl

[Lin] F. H. Lin, Nonlinear theory of defects in nematic liquid crystals, phase transition and flow phenomena, Comm. Pure Appl. Math. 42 (1989), 789-814. | MR | Zbl

[Mak] V. Makarov, On a certain class of discrete Lobachevsky space groups with infinite fundamental domain of finite measure, Soviet Math. Dokl. 7 (1966), 328-331. | MR | Zbl

[Mar] G. Margulis, Discrete groups of motions of manifolds of nonpositive curvature, AMS Translations 109 (1977), 33-45. | Zbl

[Mos] G. D. Mostow, On a remarkable class of polyhedra in complex hyperbolic space, Pac. J. Math. 86 (1980), 171-276. | MR | Zbl

[Mi] K. Miller, Three circles theorems in partial differential equations and applications to improperly posed problems, Arch. for Rat. Mech. and Anal. 16 (1964), 126-154. | MR | Zbl

[Mo] C. B. Morrey, Multiple integrals in the calculus of variations, Springer-Verlag, New York, 1966. | MR | Zbl

[N] I. G. Nikolaev, Solution of Plateau problem in spaces with curvature ≤ K, Sib, Math. J. 20 : 2 (1979), 346-353. | MR | Zbl

[S] R. Schoen, Analytic aspects of the harmonic map problem, Math. Sci. Res. Inst. Publ. vol. 2, Springer, Berlin, 1984, 321-358. | MR | Zbl

[Se] A. Selberg, Recent developments in the theory of discontinuous groups of motions of symmetric spaces, Springer Lecture Notes 118 (1970), 99-120. | MR | Zbl

[Ser] J. P. Serre, Trees, Springer Verlag, 1980. | MR | Zbl

[Sim] C. Simpson, Integrality of rigid local systems of rank two on a smooth projective variety, preprint.

[Siu] Y. T. Siu, The complex analyticity of harmonic maps and the strong rigidity of compact Kähler manifolds, Ann. of Math. 112 (1980), 73-112. | MR | Zbl

[Ste] K. Stein, Analytische Zerlegungen komplexer Räume, Math. Ann. 132 (1956), 63-93. | MR | Zbl

[SU] R. Schoen and K. Uhlenbeck, A regularity theory for harmonic maps, J. Diff. Geom. 17 (1982), 307-335. | MR | Zbl

[SY] R. Schoen and S. T. Yau, Harmonic maps and the topology of stable hyper-surfaces and manifolds of nonnegative Ricci curvature, Comment. Math. Helv. 39 (1976), 333-341. | MR | Zbl

[V] E. Vinberg, Discrete groups generated by reflections in Lobachevsky spaces, Math. USSR-Sb 1 (1967), 429-444. | Zbl

[Z] W. P. Ziemer, Weakly Differentiable Functions, Springer-Verlag, Grad. Texts in Math., 1989. | MR | Zbl

[Zim] R. J. Zimmer, Ergodic Theory and Semi-simple Groups, Birkhäuser, Boston, Basel, Stuttgart, 1984. | MR | Zbl