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Some isoperimetric inequalities and eigenvalue estimates in weighted manifolds |
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| Authors: | M Batista MP Cavalcante J Pyo |
| Institution: | 1. Instituto de Matemática, Universidade Federal de Alagoas, Maceió, AL, CEP 57072-970, Brazil;2. Department of Mathematics, Pusan National University, Busan 609-735, Republic of Korea |
| Abstract: | In this paper we prove general inequalities involving the weighted mean curvature of compact submanifolds immersed in weighted manifolds. As a consequence we obtain a relative linear isoperimetric inequality for such submanifolds. We also prove an extrinsic upper bound to the first non-zero eigenvalue of the drift Laplacian on closed submanifolds of weighted manifolds. |
| Keywords: | Isoperimetric inequality Eigenvalue estimates Weighted manifolds |
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