Complete Hypersurfaces with Constant Mean Curvature and Finite Total Curvature |
| |
| Authors: | P. Bérard M. do Carmo W. Santos |
| |
| Affiliation: | (1) Institut Fourier, UMR 5582, Université Joseph Fourier –, CNRS, B.P. 74, 38402 Saint Martin d'Hères Cedex, France;(2) I.M.P.A., Estrada Dona Castorina 110, Jardim Botânico, 22460-320 Rio de Janeiro, Brazil;(3) Departamento de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21944 Rio de Janeiro, Brazil |
| |
| Abstract: | The main result of this paper states that the traceless second fundamental tensor A0 of an n-dimensional complete hypersurface M, with constant mean curvature H and finite total curvature,  M |A0|n dvM <  , in a simply-connected space form  (c), with non-positive curvature c, goes to zero uniformly at infinity. Several corollaries of this result are considered: any such hypersurface has finite index and, in dimension 2, if H2 + c > 0, any such surface must be compact. |
| |
| Keywords: | constant mean curvature finite total curvature |
| 本文献已被 SpringerLink 等数据库收录！ |
|
