Abstract:
RESUMO: Nesta dissertação, são estudadas estimativas para o primeiro autovalor de operador
p-Laplaciano em variedades Riemannianas suaves, completas e sem bordo. Tais resultados
são extensões de resultados clássicos obtidos por Cheng, Faber-Krahn, Lichnerowicz-
Obata, Cheeger e Buser para o operador Laplace-Beltrami. O trabalho aqui desenvolvido
baseia-se no artigo "First eigenvalue for the p-Laplace operator " de Ana-Maria Matei
(Nonlinear Analysis, vol.39 (2000), p. 1051-1068). ABSTRACT: In this dissertation, estimates are studied for the rst eigenvalue of the operator p-
Laplacian on complete smooth Riemannian manifolds, without boundary. These results
are extensions of classical results obtained by Cheng, Faber-Krahn, Lichnerowicz-Obata,
Cheeger and Buser for the Laplace-Beltrami operator. The analysis presented here is
based on the article "First eigenvalue for the p-Laplace operator " Ana-Maria Matei
(Nonlinear Analysis, vol.39 (2000), p. 1051-1068).
