Publications (up to 2008)

1988 - On the Values of Gauss Map of a Complete Minimal Surface in R³ (with H. Rosenberg), Commentary Mathematical Helvetici, 63, 579-586. Ed. Birkäuser Verlag, Basel.

1989 - The Dirichlet Problem for Minimal Surface Equation on Unbounded Planar Domains (with H. Rosenberg), Journal de Mathématiques Pures et Appliquées, 68, 163-183. Ed. Gauthiers-Villars.

1991 - Geometric Configurations of Constant Mean Curvature Surfaces with Planar Boundary (with F. Braga Brito), Anais da Academia Brasileira de Ciências , 63, No. l, 5-19. Ed. An. Acad. Bras. Ci.

1991 - Some Structure Theorems for Complete Constant Mean Curvature Surfaces with Boundary a Convex Curve (with H. Rosenberg), Proceedings of the American Mathematical Society, 113, No. 4, 1045-1053. Ed. Amer. Math. Soc.

1991 - Structure Theorems for Constant Mean Curvature Surfaces Bounded by Planar Curve (with F. Braga Brito, W.Meeks III, e H. Rosenberg), Indiana University Mathematics Journal, 40, No.1 , 333-343. Ed. Ind. Univ. Math. J. .

1991 - Some Remarks on Surfaces of Prescribed Mean Curvature (with H. Rosenberg), Differential Geometry (in honor of Prof. Manfredo P. do Carmo), Pitman Monographs and surveys in Pure and applied Mathematics, 123- 148, 1991.

1992 - Recents Developments on the Structure of Compact Surfaces with Planar Boundary, The Problem of Plateau (ed. Th. Rassias), World Scientific, 245-257.

1993 - A Note on Special Surfaces in R³ (with E. Toubiana). Atas da VIII Escola de Geometria, Matemática Contemporânea, 4, pgs 108-118. Ed. Soc. Bras. Mat.

1994 - The Geometry of Properly Embedded Special Surfaces in R³ ; e.g., Surfaces Satisfying: aH + bK = 1, where a and b are Positive (with H. Rosenberg). Duke Mathematical Journal., 73, No. 2, 291-306. Ed. Duke Univ. Press.

1995 - New Results on Prescribed Mean Curvature Hypersurfaces in Hⁿ⁺¹ (with J.L.Barbosa). Anais da Academia Brasileira de Ciências., 67, No. 1,1-5. Ed. Anais Acad. Bras. Ci.

1995 - Sur les Surfaces de Weingarten Spéciales de Type Minimale (with E. Toubiana). Boletim da Sociedade Brasileira de Matemática, 26, No. 2, 129-148. Ed. Soc. Bras. Mat.

1996 - Some Properties of Hypersurfaces of Prescribed Mean Curvature in Hⁿ⁺¹ (with B. Nelli). Bulletin des Sciences Mathématiques, 120, 537-553. Ed. Gauthiers-Villars.

1997 - Special Weingarten Surfaces with Boundary a Round Circle (with F. Braga Brito). Annales de la Faculté de Science de Toulouse, VI, No. 2, 243-255. Ed. Université Paul Sabatier, Toulouse, France.

1997 - Introduction à la Geométrie Hyperbolique et aux Surfaces de Riemann. Ed.Diderot Multimedia, pgs 1- 234, Paris.

1998 - Geometric Methods and Nonlinear Analysis in Hyperbolic Space (With J. L. Barbosa) X Escola de Geometria Diferencial, UFMG, 20-24 julho.

1998 - Prescribed Mean Curvature Hypersurfaces in Hⁿ⁺¹ with Convex Planar Boundary I, (with Lucas Barbosa). Geometriae Dedicata 71, 61-74. Kluwer Academic Publishers, Netherlands.

1998 - Prescribed Mean Curvature Hypersurfaces in Hⁿ⁺¹ with Convex Planar Boundary II (with J. L. Barbosa). Séminaire de Théorie Spectrale et Géométrie de l'Institut Fourier, 16, 43-79. Grénoble, França.

1999 - New Constructions of Special Weingarten Surfaces in Hyperbolic Space (with E Toubiana), Complex Analysis in Several Variables , ed. Th. Rassias, Hadronic Press, Inc., Florida, U.S.A., 123-133.

1999 - Some Problems in Analysis and Geometry (with Th. Rassias), Complex Analysis in Several Variables, ed. Th.Rassias, Hadronic Press, Inc., Florida, U.S.A., 111-123.

1999 - On two Mean Curvature Equations in Hyperbolic Space, New Approaches in Nonlinear Analysis, ed. Th.Rassias Hadronic Press, Inc., Florida, U.S.A., 171-182.

1999 - Some Applications of Maximum Principle to Hypersurfaces in Euclidean and Hyperbolic Space (with E. Toubiana), New Approaches in Nonlinear Analysis, ed. Th. Rassias Hadronic Press, Inc., Florida, U.S.A., 183- 203.

1999 - Classification des Surfaces Speciales de Revolution de Type Delaunay. American Journal of Mathematics, 121 , No. 3, 671-700. John Hopkins University Press.

1999 - Symmetry of Properly Embedded Special Weingarten Surfaces in H³,(with E. Toubiana). Transactions of the American Mathematical Society, 352, No. 12, 4693-4711. American Mathematical Society.

2000 - Existence and Uniqueness of Minimal Graphs in Hyperbolic Space (with Eric Toubiana) . Asian Journal of Mathematics (new Journal), 4 , No. 3 , 669-694. International Press.

2001 - On the Geometry of Constant Mean Curvature One Surfaces in Hyperbolic Space (with E. Toubiana). Illinois Journal of Mathematics. 45, No 2, 371-401.

2001 - A Weierstrass-Kenmotsu Formula For Prescribed Mean Curvature Surfaces In Hyperbolic Space (with E. Toubiana). Séminaire de Théorie Spectrale et Géométrie de l'Institut Fourier de Grenoble, 19, 9-23.

2001- Variants on Alexandrov Reflection Principle and other applications of Maximum Principle (with Eric Toubiana). Séminaire de Théorie Spectrale et Géométrie de l'Institut Fourier de Grenoble, 19, 93-121.

2002- Discrete and non-Discrete Isometric Deformations of Surfaces in R³ (with Eric Toubiana). Sibirskii Mathematicheskii Zhurnal 43, No. 4, 887-893 (em russo).

2002- Discrete and non-Discrete Isometric Deformations of Surfaces in R³ (with Eric Toubiana). Siberian Mathematical Journal 43, No. 4, 714-719.

2002 Análise Complexa e Geometria Diferencial de certas superfícies no espaço hiperbólico. Boletim da Sociedade Paranaense de Matemática, 20, 1/2, 1-21.

2003 Meromorphic data for mean curvature one surfaces in hyperbolic space , II (with Eric Toubiana ), Clay Mathematics Proceedings (Mathematical Sciences Research Institute Publications : Summer School on Minimal Surfaces), 3, 521- 540.

2004- Meromorphic data for mean curvature one surfaces in hyperbolic three space (with Eric Toubiana), Tohoku Mathematical Journal, 56, No. 1, 27-56.

2005- A Note on Surfaces with Prescribed Oriented Euclidean Gauss Map (with Eric Toubiana). International Journal of Mathematics and Mathematical Sciences, No 4, 537- 544, 2005.

2005- Screw Motions Surfaces in H² × R and in S² × R (with Eric Toubiana). Illinois Journal of Mathematics, 49, No. 4, 1323-1362.

2005- Existence and non-existence results for a mean curvature equation in hyperbolic space (with E. M. Guio). Communications on Pure and Applied Analysis (CPAA), 4, No 3, 549-568. Errata corrige to Existence and non-existence for a mean curvature equation in hyperbolic space: CPAA, 7 N.2, 465, 2008.

2005- Meromorphic data for mean curvature one surfaces in hyperbolic space , II (with Eric Toubiana ). Global Theory of Minimal Surfaces . Editor: D. Hoffman. Série Clay Mathematics Proceedings, 2 American Math. Soc., 635-654.

2008- Uniqueness of H-surfaces in H²×R, H≤ ½, with boundary one or two parallel horizontal circles (with B. Nelli, E. Toubiana, W. Santos). Annals of Global Analysis and Geometry, 2, No. 4, 307-321. Published online October 2007.

2008- Associate and conjugate minimal immersions in M²× R (with L. Hauswirth and E. Toubiana). Tohoku Mathematical Journal, 60, 267-286.

2008- An asymptotic theorem for minimal surfaces and existence results for minimal graphs in H² × R (with E. Toubiana). Mathematische Annalen 342: 309-331, DOI 10.1007/s00208-008-0237-0. Published on line, May 2008,

2008- Parabolic and hyperbolic screw motion surfaces in H² × R. Journal of the Australian Mathematical Society, 85 :113-143, DOI 10.1017/S1446788708000013.

2008 - Introduction à la Geométrie Hyperbolique et aux Surfaces de Riemann (with Eric Toubiana). To appear, Cassini (ed.), Paris (second edition): http://www.cassini.fr/

Others Publications

1992 - Aspectos Comuns da Matemática, da Metafísica e das Artes. Revista Unimar vol.1, no.14, 76-93.

1992 - Invariantes Metafísicos - Considerações sobre o Ser. Semina Revista Cultural da Universidade de Londrina, Ci.Soc./Hum.v.13, no.3, 186-194.

1993 - Uma Fórmula do Fluxo para Superfícies Compactas de Curvatura Média Constante em R³ with Bordo Planar.Unimar, Paraná ,vol. 15 no. 3, 229-247.

2000- Um modelo não planar para o insight (com A. Barreto); Actia Scientiarum, vol 22, no 5, 1399-1403.

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