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 |
Acceso al artículo completo |