Abstract
R'esum'eWe investigate the question of sharp upper bounds for the Steklov eigenvalues of a hypersurface of revolution in Euclidean space with two boundary components, each isometric to $${\mathbb {S}}^{n-1}$$
S
n
-
1
. For the case of the first non zero Steklov eigenvalue, we give a sharp upper bound $$B_n(L)$$
B
n
(
L
)
(that depends only on the dimension $$n \ge 3$$
n
≥
3
and the meridian length $$L>0$$
L
>
0
) which is reached by a degenerated metric $$g^*$$
g
∗
that we compute explicitly. We also give a sharp upper bound $$B_n$$
B
n
which depends only on n. Our method also permits us to prove some stability properties of these upper bounds.
Publisher
Springer Science and Business Media LLC
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