On a Bernstein inequality for eigenfunctions

Stefano Decio, Eugenia Malinnikova

Let ${\phi }_{\lambda }$ be an eigenfunction of the Laplace-Beltrami operator on a smooth compact Riemannian manifold $(M,g)$, i.e., ${\Delta }_g{\phi }_{\lambda }+\lambda {\phi }_{\lambda }=0$. We show that ${\phi }_{\lambda }$ satisfies a local Berns…