期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：1982
卷号：79
期号：12
页码：3931-3932
DOI：10.1073/pnas.79.12.3931
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Mean curvature is one of the simplest and most basic of local differential geometric invariants. Therefore, closed hypersurfaces of constant mean curvature in euclidean spaces of high dimension are basic objects of fundamental importance in global differential geometry. Before the examples of this paper, the only known example was the obvious one of the round sphere. Indeed, the theorems of H. Hopf (for immersion of S2 into E3) and A. D. Alexandrov (for imbedded hypersurfaces of En) have gone a long way toward characterizing the round sphere as the only example of a closed hypersurface of constant mean curvature with some added assumptions. Examples of this paper seem surprising and are constructed in the framework of equivariant differential geometry.
