Abstract:

I shall present some results in global harmonic analysis that concern properties of  eigenfunctions  on compact Riemannian manifolds. Using local arguments we can show that norms of  eigenfunctions  over the entire manifold are saturated if and only if there are small balls (if is large) or small tubular neighborhoods of geodesics (if is small) on which the  eigenfunctions  have very large mass. Neither can occur on manifolds of nonpositive curvature, or, more generally, on manifolds without conjugate points.