  We consider the Jacobi operator, defined on a closed oriented hypersurfaces
immersed in the Euclidean space with the same volume of the unit sphere. We
show a local generalization for the classical result of the Willmore functional
for the Euclidean sphere. As a consequence, we prove that the first eigenvalue
of the Jacobi operator in the Euclidean sphere is a local maximum and this
result is a global one in the closed oriented surfaces space of $\mathbb{R}^3$
and genus zero.
