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

2023/05/19 by Silva, Cristiano S., Miranda, Juliana F. R., Filho, Marcio C. Araújo
#Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2305.12024

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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