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arXiv · 2305.12024

Inequalities for eigenvalues of operators in divergence form on Riemannian manifolds isometrically immersed in Euclidean space

Cristiano S. Silva·Juliana F. R. Miranda·Marcio C. Araújo Filho
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Abstract

In this paper, we compute universal inequalities of eigenvalues of a large class of second-order elliptic differential operators in divergence form, that includes, e.g., the Laplace and Cheng-Yau operators, on a bounded domain in a complete Riemannian manifolds isometrically immersed in Euclidean space. A key step in order to obtain the sequence of our estimates is to get the right Yang-type first inequality. We also prove some inequalities for manifolds supporting some special functions and tensors.

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Cristiano S. Silva, Juliana F. R. Miranda, Marcio C. Araújo Filho. 2023-05-19. Inequalities for eigenvalues of operators in divergence form on Riemannian manifolds isometrically immersed in Euclidean space. https://arxiv.org/abs/2305.12024

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