We develop new techniques for studying concentration of Laplace eigenfunctions ϕ λ as
their frequency, λ, grows. The method consists of controlling ϕ λ⁢(x) by decomposing ϕ λ …

Let (M, g) be a smooth, compact Riemannian manifold, and let {ϕ h} be an L 2-normalized
sequence of Laplace eigenfunctions,− h 2 Δ g ϕ h= ϕ h. Given a smooth submanifold H⊂ M …

This work concerns $ L^ p $ norms of high energy Laplace eigenfunctions, $(-\Delta_g-
\lambda^ 2)\phi_\lambda= 0$, $\|\phi_\lambda\| _ {L^ 2}= 1$. In 1988, Sogge gave optimal …

Let uh be a sequence of L 2-normalized semiclassical Schrödinger eigenfunctions
associated to a defect measure μ. Many recent work (Sogge, 2011; Sogge and Zelditch …

Let {ej} be an orthonormal basis of Laplace eigenfunctions of a compact Riemannian
manifold (M, g). Let H⊂ M be a submanifold and {ψ k} be an orthonormal basis of Laplace …

Let $(M, g) $ be a smooth, compact Riemannian manifold and ${\lbrace\phi\lambda\rbrace}
$ an $ L^ 2$-normalized sequence of Laplace eigenfunctions, $-\Delta_g\phi_\lambda …

Let (M, g) be a compact Riemannian surface with nonpositive sectional curvature and let γ γ
be a closed geodesic in M. And let e_ λ e λ be an L^ 2 L 2-normalized eigenfunction of the …

This book aims to explain the concepts behind the geodesic beam method that we have
developed to study the behavior of high energy eigenfunctions. The idea for geodesic …

Geodesic biangles and Fourier coefficients of restrictions of eigenfunctions Page 1 PURE and
APPLIED ANALYSIS msp EMMETT L. WYMAN, YAKUN XI AND STEVE ZELDITCH GEODESIC …

Burq-G\'erard-Tzvetkov and Hu established $ L^ p $ estimates for the restriction of Laplace-
Beltrami eigenfunctions to submanifolds. We investigate the eigenfunctions of the Schr\" …