Fundamental tone estimates for elliptic operators in divergence form and geometric applications
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| Formato: | Artículo científico |
| Lenguaje: | en |
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Academia Brasileira de Ciências
2006
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| _version_ | 1876445729869791232 |
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| author | Luquésio P. Jorge |
| author_facet | Luquésio P. Jorge |
| contents | Fundamental tone estimates for elliptic operators in divergence form and geometric applications Luquésio P. Jorge Barnabé P. Lima José F. Montenegro Greogório P. Bessa Multidisciplinaria (Ciencias Naturales y Exactas) Lr operator fundamental tone extrinsic radius th mean curvature Cheeger´s constant We establish a method for giving lower bounds for the fundamental tone of elliptic operators indivergence form in terms of the divergence of vector fields. We then apply this method to the Lroperator associated to immersed hypersurfaces with locally bounded (r + 1)-th mean curvatureHr+1 of the space forms Nn+1(c) of constant sectional curvature c. As a corollary we give lowerbounds for the extrinsic radius of closed hypersurfaces of Nn+1(c) with Hr+1 > 0 in terms of ther -th and (r + 1)-th mean curvatures. Finally we observe that bounds for the Laplace eigenvaluesessentially 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). 2006 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32778301 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.3 Vol.78 |
| format | Artículo científico |
| id | redalyc_32778301 |
| institution | Redalyc |
| language | en |
| publishDate | 2006 |
| publisher | Academia Brasileira de Ciências |
| spellingShingle | Fundamental tone estimates for elliptic operators in divergence form and geometric applications Luquésio P. Jorge Multidisciplinaria (Ciencias Naturales y Exactas) Lr operator fundamental tone extrinsic radius th mean curvature Cheeger´s constant Fundamental tone estimates for elliptic operators in divergence form and geometric applications Luquésio P. Jorge Barnabé P. Lima José F. Montenegro Greogório P. Bessa Multidisciplinaria (Ciencias Naturales y Exactas) Lr operator fundamental tone extrinsic radius th mean curvature Cheeger´s constant We establish a method for giving lower bounds for the fundamental tone of elliptic operators indivergence form in terms of the divergence of vector fields. We then apply this method to the Lroperator associated to immersed hypersurfaces with locally bounded (r + 1)-th mean curvatureHr+1 of the space forms Nn+1(c) of constant sectional curvature c. As a corollary we give lowerbounds for the extrinsic radius of closed hypersurfaces of Nn+1(c) with Hr+1 > 0 in terms of ther -th and (r + 1)-th mean curvatures. Finally we observe that bounds for the Laplace eigenvaluesessentially 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). 2006 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32778301 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.3 Vol.78 |
| title | Fundamental tone estimates for elliptic operators in divergence form and geometric applications |
| topic | Multidisciplinaria (Ciencias Naturales y Exactas) Lr operator fundamental tone extrinsic radius th mean curvature Cheeger´s constant |
| url | https://www.redalyc.org/articulo.oa?id=32778301 |