Document Zbl 0515.53042

Complete minimal varieties in hyperbolic space. (English) Zbl 0515.53042

Invent. Math. 69, 477-494 (1982).

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MSC:

53C42	Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C65	Integral geometry
49Q15	Geometric measure and integration theory, integral and normal currents in optimization

Keywords:

minimizing current; hyperbolic space; asymptotic boundary at infinity; injectivity radius

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Full Text: DOI EuDML

References:

[1]	Anderson, M.T.: Complete Minimal Hypersurfaces in Hyperbolic Manifolds (preprint)
[2]	Anderson, M.T.: On Area-Minimizing Hypersurfaces in Manifolds of Non-negative Curvature (preprint) · Zbl 0569.53023
[3]	Bakelman, I.Y.: Geometric Problems in Quasilinear Elliptic Equations. Russian Math. Surveys,25(3), 45-109 (1970) · doi:10.1070/RM1970v025n03ABEH003802
[4]	BC. Bishop, R., Crittenden, R.: Geometry of Manifolds. Pure and Applied Math., vol. 15. New York: Academic Press 1964 · Zbl 0132.16003
[5]	Bombieri, E., DeGiorgi, E., Giusti, E.: Minimal Cones and the Bernstein Problem. Invent. math.7, 243-269 (1968) · Zbl 0183.25901 · doi:10.1007/BF01404309
[6]	CY. Cheng, S.Y., Yau, S.T.: Maximal Space-like Hypersurfaces in Minkowski space. Ann. of Math.104, 407-419 (1976) · Zbl 0352.53021 · doi:10.2307/1970963
[7]	Eberlein, P., O’Neill, B.: Visibility manifolds. Pac. J. of Math.46, 45-109 (1973) · Zbl 0264.53026
[8]	Federer, H.: Geometric Measure Theory. Berlin, Heidelberg, New York: Springer 1969 · Zbl 0176.00801
[9]	Federer, H.: Some theorems on integral currents. Trans. A.M.S.117, 43-67 (1965) · Zbl 0136.18204 · doi:10.1090/S0002-9947-1965-0168727-0
[10]	Fischer-Colbrie, D., Schoen, R.: The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature. Comm. Pure and Appl. Math.33, 199-211 (1980) · Zbl 0439.53060 · doi:10.1002/cpa.3160330206
[11]	Federer, M., Fleming, W.: Normal and integral currents. Ann. of Math.72, 458-520 (1960) · Zbl 0187.31301 · doi:10.2307/1970227
[12]	Gilbarg, D., Trudinger, N.S.: Elliptic Partial Differential Equations of Second Order. Berlin, Heidelberg, New York: Springer 1977 · Zbl 0361.35003
[13]	Harvey, R., Lawson, H.B., Jr.: Calibrated Geometries (preprint) · Zbl 0584.53021
[14]	Lawson, H.B., Jr.: Minimal Varieties in Real and Complex Geometry. University of Montreal Press, 1973
[15]	Lawson, H.B., Jr.: Minimal Varieties. Proc. Symp. Pure Math. vol.27, A.M.S. Publications 1975 · Zbl 0328.49020
[16]	Lawson, H.B., Jr.: The equivariant Plateau problem and interior regularity. Trans. A.M.S.173, 231-249 (1972) · Zbl 0279.49043 · doi:10.1090/S0002-9947-1972-0308905-4
[17]	Morgan, F.: On the Singular Structure of Area Minimizing Surfaces in ? n (preprint) · Zbl 0549.49029
[18]	Meeks, W.H. III, Yau, S.-T.: Topology of three dimensional manifolds and the embedding problems in minimal surface theory. Annals of Math.112, 441-484 (1980) · Zbl 0458.57007 · doi:10.2307/1971088
[19]	Serrin, J.: The problem of Dirichlet for quasilinear elliptic equations with many independent variables. Phil. Trans. Royal Soc. London, 413-496 (1969) · Zbl 0181.38003
[20]	SU. Sachs, J., Uhlenbeck, K.: Minimal immersions of Riemann surfaces in Riemannian manifolds (preprint)
[21]	Schoen, R., Yau, S.T.: Existence of incompressible minimal surfaces and the topology of 3-manifolds with non-negative scalar curvature. Ann. of Math.110, 127-142 (1979) · Zbl 0431.53051 · doi:10.2307/1971247
[22]	Treibergs, A.: Thesis, Stanford University, 1980

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