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Title in Portuguese: Fundamental tone estimates for elliptic operators in divergence form and geometric applications
Author: Bessa, Gregório Pacelli Feitosa
Jorge, Luquésio Petrola de Melo
Lima, Barnabé Pessoa
Montenegro, José Fábio Bezerra
Keywords: Operadores elípticos
Issue Date: 2006
Citation: BESSA, G. P. F. ; JORGE, L. P. M. ; LIMA, B. P. ; MONTENEGRO, J. F. B. (2006)
Abstract: We establish a method for giving lower bounds for the fundamental tone of elliptic operators in divergence form in terms of the divergence of vector fields. We then apply this method to the Lr operator associated to immersed hypersurfaces with locally bounded (r + 1)-th mean curvature Hr+1 of the space forms Nn+1(c) of constant sectional curvature c. As a corollary we give lower bounds for the extrinsic radius of closed hypersurfaces of Nn+1(c) with Hr+1 > 0 in terms of the r -th and (r + 1)-th mean curvatures. Finally we observe that bounds for the Laplace eigenvalues essentially bound the eigenvalues of a self-adjoint elliptic differential operator in divergence form. This allows us to show that Cheeger’s constant gives a lower bounds for the first nonzero Lr - eigenvalue of a closed hypersurface of Nn+1(c).
Description: BESSA, Gregório Pacelli Feitosa ; JORGE, Luquésio Petrola de Melo ; LIMA, Barnabé Pessoa ; MONTENEGRO, José Fábio Bezerra. Fundamental tone estimates for elliptic operators in divergence form and geometric applications. Anais da Academia Brasileira de Ciências, Rio de Janeiro, v. 78, n. 3, p. 391-404, 2006.
metadata.dc.type: Artigo de Periódico
Appears in Collections:DMAT - Artigos publicados em revista científica

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