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On the first eigenvalue of the linearized operator of ther-th mean curvature of a hypersurface |
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| Authors: | Hilario Alencar Manfredo do Carmo and Harold Rosenberg |
| Institution: | (1) Departamento de Matemática, Universidade Federal de Alagoas, 57080 Maceió, AL, Brasil;(2) Instituto de Matemática Pura e Aplicada (IMPA), Estrada D. Castorina, 110, 22460 Rio de Janeiro, RJ, Brasil;(3) Department de Mathematiques, Université Paris VII, 2 Place Jussieu, 72251 Paris, Cedex 05, France |
| Abstract: | We generalize Reilly's inequality for the first eigenvalue of immersed submanifolds ofIR m +1 and the total (squared) mean curvature, to hypersurfaces ofIR m +1 and the first eigenvalue of the higher order curvatures. We apply this to stability problems. We also consider hypersurfaces in hyperbolic space. |
| Keywords: | Curvatures of hypersurfaces Reilly's inequality stability |
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