Boundedness of Laplacian eigenfunctions on manifolds of infinite volume

Leonardo Bonorino, Patrícia Klaser, Miriam Telichevesky

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} \l…