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

H.F. de Lima ^[1] ; A.F. de Sousa ^[2] ; F.R. dos Santos ^[1] ; M.A.L. Velásquez ^[1]
1. [1] Universidade Federal de Campina Grande
  
  Universidade Federal de Campina Grande
  
  Brasil
2. [2] Universidade Federal de Pernambuco
  
  Universidade Federal de Pernambuco
  
  Brasil
Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 31, Nº 1, 2016, págs. 68-88
Idioma: inglés
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Resumen
- Our purpose in this article is to obtain sharp upper estimates for the rst 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.