- 期刊
ON MINIMAL HYPERSURFACES OF NONNEGATIVELY RICCI CURVED MANIFOLDS
摘要
We consider a complete open riemannian manifold M of nonnegative Ricci curvature and a rectifiable hypersurface ∑ in M which satisfies some local minimizing property. We prove a structure theorem for M and a regularity theorem for ∑. More precisely, a covering space of M is shown to split off a compact domain and ∑ is shown to be a smooth totally geodesic submanifold. This generalizes a theorem due to Kasue and Meyer.
延伸閱讀
- Ianus, S., & Vîlcu, G. E. (2008). Hypersurfaces of Paraquaternionic Space forms. Journal of Generalized Lie Theory and Applications, 2(3), 175-179. https://www.airitilibrary.com/Article/Detail?DocID=17365279-200809-201012090046-201012090046-175-179
- 林鼎盛（2010）。Bifurcation studies in a electrical hydrodynamic nonlinear dynamical system〔碩士論文，國立臺灣大學〕。華藝線上圖書館。https://doi.org/10.6342/NTU.2010.03144
- Wang, Z., Pei, D., Chen, L., Kong, L., & Han, Q. (2012). Singularities of Focal Surfaces of Null Cartan Curves in Minkowski 3-Space. Abstract and Applied Analysis, 2012(), 911-930-661. https://doi.org/10.1155/2012/823809
- SONIS, M. (2000). Critical Bifurcation Surfaces of 3D Discrete Dynamics. Discrete Dynamics in Nature and Society, 2000(), ae333-343. https://doi.org/10.1155/S1026022600000315
- CAI, K., & XU, H. (2006). SPACELIKE HYPERSURFACES IN DE SITTER SPACE WITH CONSTANT HIGHER-ORDER MEAN CURVATURE. International Journal of Mathematics and Mathematical Sciences, 2006(), 258-263-019. https://doi.org/10.1155/IJMMS/2006/19545