References
S. B. Alexander, I. D. Berg andR. L. Bishop, The Riemannian obstacle problem,Ill. J. Math. 31 (1987), 167–184.
S. Agmon,Unicité et convexité dans les problèmes différentiels, Sém. d’Analyse Sup., Univ. de Montréal, 1965.
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,
K. Brown,Buildings, Springer, New York, 1989.
F. Bruhat andJ. Tits, Groupes réductifs sur un corps local. I. Données radicielles valuées,Publ. Math. IHES 41 (1972), 5–251.
K. Corlette, Archimedian superrigidity and hyperbolic geometry,Annals of Math., to appear.
Y. J. Chiang, Harmonic maps of V-manifolds,Ann. Global Anal. Geom. 8 (1990), 315–344.
P. Deligne andG. D. Mostow, Monodromy of hypergeometric functions and non-lattice integral monodromy,Publ. Math. IHES 63 (1986), 5–89.
J. Eells andJ. H. Sampson, Harmonic mappings of Riemannian manifolds,Amer. J. Math. 86 (1964), 109–160.
H. Federer,Geometric Measure Theory, Springer-Verlag, New York, 1969.
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.
H. Garland, P-adic curvature and the cohomology of discrete subgroups,Ann. of Math. 97 (1973), 375–423.
N. Garofalo andF. H. Lin, Monotonicity properties of variational integrals, A p weights and unique continuation,Indiana Math. J. 35 (1986), 245–268.
M. Gromov, P. Pansu,Rigidity of lattices: An introduction, to appear in Springer Lecture Notes.
M. Gromov andI. Piatetski-Shapiro, Non-arithmetic groups in Lobachevsky spaces,Publ. Math. IHES 66 (1988), 93–103.
H. Garland andM. S. Raghunathan, Fundamental domains for lattices inR-rank 1 groups,Ann. of Math. 92 (1970), 279–326.
M. Gromov,Partial differential relations, Springer Verlag, 1986.
R. Hamilton,Harmonic maps of manifolds with boundary, Lecture Notes471, Springer 1975.
P. Hartman, On homotopic harmonic maps,Can. J. Math. 19 (1967), 673–687.
P. de la Harpe andA. Valette,La propriété (T) de Kazhdan pour les groupes localement compacts, Astérisque175 (1989), Soc. Math. de France.
H. Karcher, Riemannian center of mass and mollifier smoothing,Comm. Pure and Appl. Math. 30 (1977), 509–541.
E. M. Landis, A three-sphere theorem,Dokl. Akad. Nauk S.S.S.R. 148 (1963), 277–279. Translated inSoviet Math. 4 (1963), 76–78.
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 inRussian Math. Surveys 18 (1963), 1–62.
M. L. Leite, Harmonic mappings of surfaces with respect to degenerate metrics,Amer. J. Math. 110 (1988), 399–412.
F. H. Lin, Nonlinear theory of defects in nematic liquid crystals, phase transition and flow phenomena,Comm. Pure Appl. Math. 42 (1989), 789–814.
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.
G. Margulis, Discrete groups of motions of manifolds of nonpositive curvature,AMS Translations 109 (1977), 33–45.
G. D. Mostow, On a remarkable class of polyhedra in complex hyperbolic space,Pac. J. Math. 86 (1980), 171–276.
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.
C. B. Morrey,Multiple integrals in the calculus of variations, Springer-Verlag, New York, 1966.
I. G. Nikolaev, Solution of Plateau problem in spaces with curvature ⩽K,Sib, Math. J. 20:2 (1979), 346–353.
R. Schoen, Analytic aspects of the harmonic map problem,Math. Sci. Res. Inst. Publ. vol.2, Springer, Berlin, 1984, 321–358.
A. Selberg, Recent developments in the theory of discontinuous groups of motions of symmetric spaces,Springer Lecture Notes 118 (1970), 99–120.
J. P. Serre,Trees, Springer Verlag, 1980.
C. Simpson,Integrality of rigid local systems of rank two on a smooth projective variety, preprint.
Y. T. Siu, The complex analyticity of harmonic maps and the strong rigidity of compact Kähler manifolds,Ann. of Math. 112 (1980), 73–112.
K. Stein, Analytische Zerlegungen komplexer Räume,Math. Ann. 132 (1956), 63–93.
R. Schoen andK. Uhlenbeck, A regularity theory for harmonic maps,J. Diff. Geom. 17 (1982), 307–335.
R. Schoen andS. T. Yau, Harmonic maps and the topology of stable hyper-surfaces and manifolds of nonnegative Ricci curvature,Comment. Math. Helv. 39 (1976), 333–341.
E. Vinberg, Discrete groups generated by reflections in Lobachevsky spaces,Math. USSR-Sb 1 (1967), 429–444.
W. P. Ziemer,Weakly Differentiable Functions, Springer-Verlag, Grad. Texts in Math., 1989.
R. J. Zimmer,Ergodic Theory and Semi-simple Groups, Birkhäuser, Boston, Basel, Stuttgart, 1984.
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Research partially by NSF grant # DMS-03076.
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Gromov, M., Schoen, R. Harmonic maps into singular spaces andp-adic superrigidity for lattices in groups of rank one. Publications Mathématiques de l’Institut des Hautes Scientifiques 76, 165–246 (1992). https://doi.org/10.1007/BF02699433
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DOI: https://doi.org/10.1007/BF02699433