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Compact hypersurfaces with constant higher order mean curvatures.

Antonio Ros Mulero (1987)

Revista Matemática Iberoamericana

A fundamental question about hypersurfaces in the Euclidean space is to decide if the sphere is the only compact hypersurface (embedded or immersed) with constant higher order mean curvature Hr, for some r = 1, ..., n.

Complete minimal surfaces in 3 with type Enneper end

Nedir Do Espirito Santo (1994)

Annales de l'institut Fourier

We show that there exists a complete minimal surface immersed into 3 which is conformally equivalent to a compact hyperelliptic Riemann surface of genus three minus one point. The end of the surface is of Enneper type and its total curvature is - 16 π .

Complete minimal surfaces in R3.

Francisco J. López, Francisco Martín (1999)

Publicacions Matemàtiques

In this paper we review some topics on the theory of complete minimal surfaces in three dimensional Euclidean space.

Complete minimal surfaces of arbitrary genus in a slab of 3

Celso J. Costa, Plinio A. Q. Simöes (1996)

Annales de l'institut Fourier

In this paper we construct complete minimal surfaces of arbitrary genus in 3 with one, two, three and four ends respectively. Furthermore the surfaces lie between two parallel planes of 3 .

Complete real Kähler Euclidean hypersurfaces are cylinders

Luis A. Florit, Fangyang Zheng (2007)

Annales de l’institut Fourier

In this note we show that any complete Kähler (immersed) Euclidean hypersurface M 2 n 2 n + 1 must be the product of a surface in 3 with an Euclidean factor n - 1 2 n - 2 .

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