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References
Almgren, F.J.: Some interior regularity theorems for minimal surfaces and an extension of Bernstein's theorem. Ann. of Math. (2),84, 277–292 (1966)
Bernstein, S.N.: Über ein geometrisches Theorem und seine Anwendung auf die partiellen Differentialgleichungen vom elliptischen Typus. Math. Z.26, 551–558 (1927)
Bombieri, E., DeGiorgi, E., Giusti, E.: Minimal cones and the Bernstein theorem. Invent. math.7, 243–269 (1969)
Cheeger, J., Ebin, D.: Comparison theorems in Riemannian geometry. Amsterdam-Oxford: North-Holland, New York: American Elsevier Publ 1975
Cheng, S.-Y.: Liouville theorem for harmonic maps, Preprint
Chern, S.-S., Goldberg, S.I.: On the volume decreasing property of a class of real harmonic mappings. Amer. J. Math.97, 133–147 (1975)
Chern, S.-S., Osserman, R.: Complete minimal surfaces in euclideann-space. J. Analyse Math19, 15–34 (1967)
Crittenden, R.: Minimum and conjugate points in symmetric spaces. Canad. J. Math.14, 320–328 (1962)
DeGiorgi, E.: Una estensione del teorema di Bernstein. Ann. Scuola Norm. Sup. Pisa19, 79–85 (1965)
Eells, J., Lemaire, L.: A report on harmonic maps. Bull. London Math. Soc.10, 1–68 (1978)
Fischer-Colbrie, D.: Some rigidity theorems for minimal submanifolds of the sphere. Preprint. To appear in Acta Math.
Frehse, J.: Essential selfadjointness of singular elliptic operators. Bol. Soc. Brasil. Mat8, 87–107 (1977)
Garber, W.-D., Ruijsenaars, S.N.M., Seiler, E., Burns, D.: On finite action solutions of the nonlinear σ-model. Ann. Physics119, 305–325 (1979)
Hildebrandt, S., Kaul, H.: Two-dimensional variational problems with obstructions, and Plateau's problem forH-surfaces in a Riemannian manifold. Comm. Pure Appl. Math.25, 187–223 (1972)
Hildebrandt, S., Widman, K.-O.: Some regularity results for quasilinear elliptic systems of second order. Math. Z.142, 67–86 (1975)
Hildebrandt, S., Widman, K.-O.: On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order. Ann. Scuola Norm. Sup. Pisa (IV),4, 145–178 (1977)
Hildebrandt, S., Kaul, H., Widman, K.-O.: An existence theorem for harmonic mappings of Riemannian manifolds. Acta Math.138, 1–16 (1977)
Hildebrandt, S.: Entire solutions of nonlinear elliptic systems, and an approach to Bernstein theorems. Lecture at the Collège de France, March 1979, to appear
Hildebrandt, S., Widman, K.-O.: Sätze vom Liouvilleschen Typ für quasilineare elliptische Gleichungen und Systeme. Nachr. Akad. Wiss. Göttingen, II. Math.-Phys. Klasse, Nr. 4, 41–59. Jahrgang 1979
Hoffman, D.A., Osserman, R.: The geometry of the generalized Gauss map. Preprint
Hoffman, D.A., Osserman, R.: The area of the generalized Gaussian image and the stability of minimal surfaces inS n and ℝn. Preprint
Ivert, P.A.: On quasilinear elliptic systems of diagonal form. Math. Z.170, 283–286 (1980)
Jensen, G.R.: Imbeddings of Stiefel manifolds into Grassmannians. Duke Math. J.42, 394–407 (1975)
Jost, J.: Eineindeutigkeit harmonischer Abbildungen. Diplomarbeit 1979
Jost, J.: Eine geometrische Bemerkung zu Sätzen über harmonische Abbildungen, die ein Dirichletproblem lösen. Manuscripta Math., in press (1980)
Karp, L.: Differential inequalities on Riemannian manifolds: Applications to isometric immersions and harmonic mappings. Preprint
Lawson, H.B., Osserman, R.: Non-existence, non-uniqueness and irregularity of solutions to the minimal surface system. Acta Math.139, 1–17 (1977)
Leichtweiss, K.: Zur Riemannschen Geometrie in Grassmannschen Mannigfaltigkeiten. Math. Z.76, 334–366 (1961)
Meier, M.: Liouville theorems for nonlinear elliptic equations and systems. Manuscripta Math.29, 207–228 (1979)
Meier, M.: Liouville theorems for nondiagonal elliptic systems in arbitrary dimensions. Preprint (1980)
Morrey, C.B.: Second order elliptic systems of differential equations. In: Contributions to the theory of partial differential equations, pp. 101–160. Ann. of Math. Studies No. 33. Princeton: Princeton University Press 1954
Morrey, C.B.: Multiple integrals in the calculus of variations. Heidelberg-New York: Springer-Verlag 1966
Moser, J.: On Harnack's theorem for elliptic differential equations. Comm. Pure Appl. Math.14, 577–591 (1961)
Osserman, R.: Minimal Varieties. Bull. Amer. Math. Soc.75, 1092–1120 (1969)
Reilly, R.: Extrinsic rigidity theorems for compact submanifolds of the sphere. J. Differential Geometry4, 487–497 (1970)
Ruh, E.A.: Asymptotic behaviour of non-parametric minimal hypersurfaces. J. Differential Geometry4, 509–513 (1970)
Ruh, E.A., Vilms, J.: The tension field of the Gauss map. Trans. Amer. Math. Soc.149, 569–573 (1970)
Schoen, R., Yau, S.-T.: Harmonic maps and the topology of stable hypersurfaces and manifolds with nonnegative Ricci curvature. Comm. Math. Helv.39, 333–341 (1976)
Simons, J.: Minimal varieties in riemannian manifolds. Ann. of Math.88, 62–105 (1968)
Wiegner, M.: A-priori Schranken für Lösungen gewisser elliptischer Systeme. Manuscripta Math.18, 279–297 (1976)
Wolf, J.A.: Spaces of constant curvature. New York: McGraw-Hill 1966
Wong, Y.-C.: Differential Geometry of Grassmann manifolds. Proc. Nat. Acad. Sci. USA57, 589–594 (1967)
Wong, Y.-C.: Sectional curvatures of Grassmann manifolds. Proc. Nat. Acad. Sci. USA60, 75–79 (1968)
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Hildebrandt, S., Jost, J. & Widman, K.O. Harmonic mappings and minimal submanifolds. Invent Math 62, 269–298 (1980). https://doi.org/10.1007/BF01389161
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DOI: https://doi.org/10.1007/BF01389161