分析和PDE讨论班——On the concentration of eigenfunctions.
主 题: 分析和PDE讨论班——On the concentration of eigenfunctions.
报告人: C. D. Sogge (Johns Hopkins University)
时 间: 2016-12-15 13:30-14:30
地 点: 理科一号楼1303
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 $L^p$ norms of eigenfunctions over the entire manifold are saturated if and only if there are small balls (if $p$ is large) or small tubular neighborhoods of geodesics (if $p$ is small) on which the eigenfunctions have very large $L^p$ mass. Neither can occur on manifolds of nonpositive curvature, or, more generally, on manifolds without conjugate points.
