Sharp Upper Estimates for the First Eigenvalue of a Jacobi Type Operator

Authors

  • H.F. de Lima Departamento de Matemática, Universidade Federal de Campina Grande, 58.429 − 970 Campina Grande, Paraı́ba, Brazil
  • A.F. de Sousa Departamento de Matemática, Universidade Federal de Pernambuco 50.740-560 Recife, Pernambuco, Brazil
  • F.R. dos Santos Departamento de Matemática, Universidade Federal de Campina Grande, 58.429 − 970 Campina Grande, Paraı́ba, Brazil
  • Marco Antonio L. Velásquez Departamento de Matemática, Universidade Federal de Campina Grande, 58.429 − 970 Campina Grande, Paraı́ba, Brazil

Keywords:

Euclidean space, Euclidean sphere, closed hypersurfaces, r-th mean curvatures, Jacobi operator, Reilly type inequalities

Abstract

Our purpose in this article is to obtain sharp upper estimates for the first positive eigenvalue of a Jacobi type operator, which is a suitable extension of the linearized operators of the higher order mean curvatures of a closed hypersurface immersed either in the Euclidean space or in the Euclidean sphere.

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References

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Published

2016-06-01

Issue

Vol. 31 No. 1 (2016)

Section

Differential Geometry

How to Cite

Sharp Upper Estimates for the First Eigenvalue of a Jacobi Type Operator. (2016). Extracta Mathematicae, 31(1), 69-88. https://revista-em.unex.es/index.php/EM/article/view/2605-5686.31.1.69

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