Prescribed mean curvature hypersurfaces in H n+1 with convex planar boundary, II
Séminaire de théorie spectrale et géométrie, Tome 16 (1997-1998), p. 43-79
@article{TSG_1997-1998__16__43_0,
     author = {Barbosa, Jo\~ao Lucas Marques and Sa Earp, Ricardo},
     title = {Prescribed mean curvature hypersurfaces in $H^{n+1}$ with convex planar boundary, II},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {16},
     year = {1997-1998},
     pages = {43-79},
     zbl = {0942.53044},
     language = {en},
     url = {http://www.numdam.org/item/TSG_1997-1998__16__43_0}
}
Barbosa, João Lucas Marques; Sa Earp, Ricardo. Prescribed mean curvature hypersurfaces in $H^{n+1}$ with convex planar boundary, II. Séminaire de théorie spectrale et géométrie, Tome 16 (1997-1998) pp. 43-79. https://www.numdam.org/item/TSG_1997-1998__16__43_0/

[1] Bakelman, I.Ya., Hypersurfaces with Given Mean Curvature and Quasilinear Elliptic Equations with Strong Nonlinearities, Mat. Sbornik 75, 604-638 ( 1968). | MR 225004 | Zbl 0176.18801

[2] Bakelman, I.Ya., Geometric Problems in Quasilinear Elliptic Equations, Russian Math. Surveys 25,45-109 ( 1970). | MR 340814 | Zbl 0217.41401

[3] Barbosa, J.L.M., Geometria Hiperbólica. 20° Colóquio Brasileiro de Matematica, ( 1995).

[4] Barbosa, J.L.M. and Colares, A.G., Stability of Hypersurfaces with Constant r-Mean Curvature, Annals of Global Analysis and Geometry, 15, 277-297, ( 1997). | MR 1456513 | Zbl 0891.53044

[5] Barbosa, J.L.M. and Sa Earp, R., New Results on Prescribed Mean Curvature Hypersurfaces in Space Forms, Anais da Acad. Bras. de Ciências 67,1-5 ( 1995). | MR 1752613 | Zbl 0828.53053

[6] Barbosa, J.L.M. and Sa Earp, R., Prescribed Mean Curvature Hypersurfaces in Hn+1 ( - l ) with Convex Planar Boundary, I. To appear in Geometriae Dedicata 71, 61-74 ( 1998). | MR 1624726 | Zbl 0922.53023

[7] Braga Brito, F. and Sa Earp, R., Geometric Configurationsof Constant Mean Curvature Surfaces with Planar Boundary, Anais da Acad. Bras. de Ciências 63, 5-19 ( 1991). | MR 1115489 | Zbl 0803.53011

[8] Braga Brito, F. and Sa Earp, R., Special Weingarten Surfaces with Boundary a Round Circle, Annales de la Faculté de Sciences de Toulouse 2 VI, 243-255 ( 1997). | Numdam | Zbl 0901.53003

[9] Braga Brito F., Meeks W.H., Rosenberg H. and Sa Earp R., Structure Theorems for Constant Mean Curvarure Surfaces Bounded by a Planar Curve, Indiana Univ. Math. J. 40,333-343 ( 1991). | MR 1101235 | Zbl 0759.53003

[10] Caffarelli L., Nirenberg L. and Spruck J., Nonlinear Second-order Eiliptic Equations V.The Dirichlet Problem for Weingarten Hypersurfaces, Comm. on Pure and Applied Math 61,47-70 ( 1988). | MR 917124 | Zbl 0672.35028

[11] Gomes, J. De M., Sobre Hipersuperflcies com Curvatura Média Constante no Espaço Hiperbólico, Doctoral thesis, IMPA, 1985.

[12] Gilbarg D. and Trudinger N.S., Elliptic Partial Differential Equations of Second Order, Springer-Verlag ( 1983). | MR 737190 | Zbl 0562.35001

[13] Guio M.E., Uma Equação do Tipo Monge-Ampère, Dissertação de Mestrado, PUC-Rio ( 1995).

[14] Kapouleas N., Compact Constant Mean Curvature Surfaces in Euclidean Three-Space, J.Diff. Geometry 33.683-715( 1991). | MR 1100207 | Zbl 0727.53063

[15] Korevaar N., Kusner R., Meeks W.H. and Solomon B., Constant Mean Curvature Surfaces in Hyperbolic Space, American J. of Math. 114, 1-143 ( 1992). | MR 1147718 | Zbl 0757.53032

[16] Kusner R.B., Global Geometry of Extremal Surfaces in Three-Space, Doctoral thesis, University of California, Berkeley ( 1985).

[17] López, R., Constant Mean Curvature Surfaces with boundary in the hyperbolic space, preprint 1996. | MR 1669875

[18] López, R., and Montiel, S., Existence of Constant Mean Curvature Graphs in Hyperbolic Space, submitted to Calculus of Variations and Partial Differential Equations. | Zbl 0945.53008

[19] López, R. and Montiel, S., Constant Mean Curvature Discs with Bounded Area, Proceedings of A.M.S. 123, 1555-1558 ( 1995). | MR 1286001 | Zbl 0840.53006

[20] Nelli, B., Hypersurfaces de Courbure Constante dans l'Espace Hyperbolique, Thèse de Doctorat, Université de Paris VII, Paris ( 1995).

[21] Nelli, B. and Rosenberg, H., Some Remarks on Embedded Hypersurfaces in Hyperbolic Space of Constant Mean Curvature and Spherical boundary, Ann. Glob. An. and Geom. 13, 23-30 ( 1995). | MR 1327108 | Zbl 0831.53039

[22] Nelli, B. and Rosenberg, H., Some remarks on Positive Scalar and Gauss-Kronecker Curvature Hypersurfaces of Rn+1 and Hn+l, Annales de l'Institut Fourier, 47, (4), 1209-1218 ( 1997). | Numdam | MR 1488250 | Zbl 0878.53007

[23] Nelli , B. and Sa Earp, R., Some Properties of Hypersurfaces of Prescribed Mean Curvature in Hn+1, Bull. Sc. Math. (6) 120, 537-553 ( 1996). | MR 1420970 | Zbl 0872.53008

[24] Nelli, B. and Semmler, B., Some Remarks on Compact Constant Mean Curvature Hypersurfaces in a Halfspace on Hn+1, to appear in the J. of Geometry. | Zbl 0981.53049

[25] Nelli, B. and Spruck, J., On the Existence and Uniqueness of Constant Mean Curvature Hypersurfaces in Hyperbolic Space, Geometric Analysis and the Calculus of Variation, ed. J. Jost, International Press, Cambridge, 253-266 ( 1996). | MR 1449411 | Zbl 0936.35069

[26] Oliker, V., The Gauss Curvature and Minkowski Problems in Space Forms, Contemporary Mathematics 101, 107-123 ( 1989). | MR 1034975 | Zbl 0689.53035

[27] Protter, M.H. and Weinberger, H.F., Maximum Principles in Differential Equations, Elglewood Cliffs, New Jersey Prentice-Hall, ( 1967). | MR 219861 | Zbl 0153.13602

[28] Rassias, T.M. and Sa Earp, R., Some Problems in Analysis and Geometry, to appear in the volume Complex Analysis in Several Variables, Hadronic Press Inc., Florida, USA, ( 1998), ed. Th. Rassias. | Zbl 0949.53003

[29] Rosenberg, H., Hypersurfaces of Constant Curvature in Space Forms, Bulletin des Sciences Mathématiques, 2° série, 117,211-239 ( 1993). | MR 1216008 | Zbl 0787.53046

[30] Ros, A. and Rosenberg, H., Constant Mean Curvature Surfaces in a Half-Space of R3 with Boundary in the Boundary of a Half-Space, J. Diff. Geometry 44, 807-817 ( 1996). | MR 1438193 | Zbl 0883.53009

[31] Rosenberg, H. and Sa Earp, R., The Geometry of ProperlyEmbedded Special Surfaces in R3; e.g., Surfaces Satisfying aH + bK = 1, where a and b are Positive, Duke Mathematical Journal, 73, (2), 291-306 ( 1994). | MR 1262209 | Zbl 0802.53002

[32] Sa Earp, R., Recent Developments on the Structure of Compact Surfaces with Planar Boundary, The Problem of Plateau (edited by Th. M. Rassias), World Scientific, 245-257 ( 1992). | MR 1209221 | Zbl 0790.53008

[33] Sa Earp, R., On two Mean Curvature Equations in Hyperbolic Space, to appear in the volume New Approches in Nonlinear Analysis, Hadronic Press Inc., Florida, USA, ( 1998), ed. Th. Rassias. | Zbl 0960.53034

[34] Sa Earp, R. and Toubiana, E., Introduction à la Géométrie Hyperbolique et aux Surfaces de Riemann, Ed. Diderot Multimedia, Paris, 1997. | Zbl 0944.30001

[35] Sa Earp, R. and Toubiana, E., Some Applications of Maximum Principle to Hypersurfaces Theory in Euclidean and Hyperbolic Space. To appear in the volume New Approches in Nonlinear Analysis, Hadronic Press Inc., Florida, USA, ( 1998), ed. Th. Rassias. | Zbl 0959.53038

[36] Sa Earp, R. and Toubiana, E., Existence and uniqueness of minimal graphs in hyperbolic space, preprint. | Zbl 0984.53005

[37] Sa Earp, R. and Toubiana, E., Symmetry of Properly Embedded Special Weingarten Surfaces in H3, to appear. | Zbl 0989.53003

[38] Schoen, R., Uniqueness, Symmetry, and Embeddedness of Minimal Surfaces, J.Diff. Geometry, 18, 791-809 ( 1983). | MR 730928 | Zbl 0575.53037

[39] Semmler, B., Surfaces de Courbure Moyenne Constante dans les Espaces Euclidien et Hyperbolic, doctorat theses, Paris VII, ( 1997).