Constant scalar curvature hypersurfaces with spherical boundary in Euclidean space.

Título inglés	Constant scalar curvature hypersurfaces with spherical boundary in Euclidean space.
Título español	Hipersuperficies de curvatura escalar constante con frontera esférica en el espacio euclídeo.
Autor/es	Alías, Luis J. ; Malacarne, J. Miguel
Organización	Dep. Mat. Univ. Murcia, Espinardo (Murcia), España;Dep. Mat. Univ. Fed. Espiruti Santo Vitoria ES, Brasil
Revista	0213-2230
Publicación	2002, 18 (2): 431-442, 18 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	It is still an open question whether a compact embedded hypersurface in the Euclidean space with constant mean curvature and spherical boundary is necessarily a hyperplanar ba1l or a spherical cap, even in the simplest case of a compact constant mean curvature surface in R3 bounded by a circle. In this paper we prove that this is true for the case of the scalar curvature. Specifica1ly we prove that the only compact embedded hypersurfaces in the Euclidean space with constant scalar curvature and spherical boundary are the hyperplanar round balIs (with zero scalar curvature) and the spherical caps (with positive constant scalar curvature). The same applies in general to the case of embedded hypersurfaces with constant r-mean curvature, with r>=2.
Clasificación UNESCO	120404
Palabras clave español	Curvatura ; Espacio euclídeo ; Inmersiones ; Hipersuperficies compactas
Código MathReviews	MR1949835
Código Z-Math	Zbl 1038.53060
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