We study complete noncompact 1-minimal stable hypersurfaces in a 4-dimensional sphere S4.We show that there is no complete noncompact 1-minimal stable hypersurfaces in S4 with polynomial volume growth and the restrict...We study complete noncompact 1-minimal stable hypersurfaces in a 4-dimensional sphere S4.We show that there is no complete noncompact 1-minimal stable hypersurfaces in S4 with polynomial volume growth and the restriction of the mean curvature and GaussKronecker curvature.These results are partial answers to the conjecture of Alencar,do Carmo and Elbert when the ambient space is a 4-dimensional sphere.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.1147114511401514)Qing Lan Projects
文摘We study complete noncompact 1-minimal stable hypersurfaces in a 4-dimensional sphere S4.We show that there is no complete noncompact 1-minimal stable hypersurfaces in S4 with polynomial volume growth and the restriction of the mean curvature and GaussKronecker curvature.These results are partial answers to the conjecture of Alencar,do Carmo and Elbert when the ambient space is a 4-dimensional sphere.
