Sobre estabilidade de hipersuperfícies com curvatura escalar nula.

• Main Author: Farias Filho, Francisco Silvio Bernardo de
• Publication Date: 2018
• Format: Master thesis
• Language: por
• Source: Repositório Institucional da Universidade Federal do Ceará (UFC)
• dARK ID: ark:/83112/001300002tq8z
• Download full: http://www.repositorio.ufc.br/handle/riufc/34725
• topic: Curvatura escalar; Curvatura de Gauss-Kronecker; Curvatura média; Estabilidade; Gráficos; Vizinhança tubular; Volume; Scalar curvature; Gauss-Kronecker Bend; Mean curvature; Stability; Graphics; Tubular neighborhood; Volume

We will prove that there are no complete and stable hypersurface of R4 with zero scalar curvature, polynomial volume growth and such that -K H3 ≥ c> 0 at any point, for some constant c> 0, where K denotes the curvature of Gauss-Kronecker and H denotes the mean curvature of the immersion x: M3 → R4, where Mn is Riemannian variety. Our second result is a Bernstein type, which guarantees that there are no complete graphs of R4 with zero scalar curvature and such that -K H3 ≥ c> 0 at every point. Finally, it will be shown that if there is a stable hypersurface with zero scalar curvature and -K H3 ≥ c> 0 at all points, that is, with volume growth higher than the polynomial, then its tubular neighborhood is not plunged by soft rays.