  In a Hadamard manifold $M$, it is proved that if $u$ is a
$\lambda$-eigenfunction of the Laplacian that belongs to $L^p(M)$ for some $p
\ge 2$, then $u$ is bounded and $\|u\|_{\infty} \le C \|u\|_p,$ where $C$
depends only on $p$, $\lambda$ and on the dimension of $M$. This result is
obtained in the more general context of a complete Riemannian manifold endowed
with an isoperimetric function $H$ satisfying some integrability condition. In
this case, the constant $C$ depends on $p,\lambda$ and $H.$
