Use este identificador para citar ou linkar para este item: http://www.repositorio.ufc.br/handle/riufc/3792
Título: Eigenvalue and "twisted" eigenvalue problems, applications to CMC surfaces
Autor(es): Barbosa, João Lucas Marques
Berard, Pierre
Palavras-chave: Autovalores
Isometria (Matemática)
Geometria
Data do documento: 2000
Editor: Journal de Mathématiques Pures et Appliquées
Citação: BARBOSA, J. L. M. ; BERARD, P. (2000)
Abstract: In this paper we investigate an eigenvalue problem which appears naturally when one considers the second variation of a constant mean curvature immersion. In this geometric context, the second variation operator is of the form Δg+b, where b is a real valued function, and it is viewed as acting on smooth functions with compact support and with mean value zero. The condition on the mean value comes from the fact that the variations under consideration preserve some balance of volume. This kind of eigenvalue problem is interesting in itself. In the case of a compact manifold, possibly with boundary, we compare the eigenvalues of this problem with the eigenvalues of the usual (Dirichlet) problem and we in particular show that the two spectra are interwined (in fact strictly interwined generically). As a by-product of our investigation of the case of a complete manifold with infinite volume we prove, under mild geometric conditions when the dimension is at least 3, that the strong and weak Morse indexes of a constant mean curvature hypersurface coincide.
Descrição: BARBOSA, J. L. M. ; BERARD, P. Eigenvalue and "twisted" eigenvalue problems, applications to CMC surfaces. Journal de Mathématiques Pures et Appliquées, França, v. 79,´p. 427-450, 2000.
URI: http://www.repositorio.ufc.br/handle/riufc/3792
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