Uniqueness of starshaped compact hypersurfaces with prescribed m-th mean curvature in hyperbolic space

• Autor(a) principal: Barbosa, João Lucas Marques
• Data de Publicação: 2007
• Outros Autores: Lira, Jorge Herbert Soares de, Oliker, Vladimir I.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da Universidade Federal do Ceará (UFC)
• Texto Completo: http://www.repositorio.ufc.br/handle/riufc/3797
• topic: Hipersuperfícies; Espaços hiperbólicos

Let ψ be a given function defined on a Riemannian space. Under what conditions does there exist a compact starshaped hypersurface M for which ψ , when evaluated on M,coincides with the m-th elementary symmetric function of principal curvatures of M for a given m? The corresponding existence and uniqueness problems in Euclidean space have been investigated by several authors in the mid 1980s. Recently,conditions for existence were established in elliptic space and, most recently, for hyperbolic space. However, the uniqueness problem has remained open. In this paper we investigate the problem of uniqueness in hyperbolic space and show that uniqueness (up to a geometrically trivial transformation) holds under the same conditions under which existence was established.