The structure of weakly stable minimal hypersurfaces

Anais da Academia Brasileira de Ciências

Xu Cheng²  Leung-fu Cheung¹  Detang Zhou² 

[1] ,Universidade Federal Fluminense Instituto de Matemática Niterói RJ ,Brasil

关键词: minimal hypersurfaces;    weak stability;    ends;    hipersuperfícies mínimas;    estabilidade fraca;    fins;   

DOI  :  10.1590/S0001-37652006000200001

来源: SciELO

【 摘 要 】

In this short communication, we announce results from our research on the structure of complete noncompact oriented weakly stable minimal hypersurfaces in a manifold of nonnegative sectional curvature. In particular, a complete oriented weakly stable minimal hypersurface in Rm, m > 4, must have only one end; any complete noncompact oriented weakly stable minimal hypersurface has only one end if the complete oriented ambient manifold Nm, m > 7, has nonnegative sectional curvature and Ricci curvature bounded below by a positive constant; a complete oriented weakly stable minimal hypersurface in Rm, m > 4, with finite total scalar curvature is a hyperplane.

【 授权许可】

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