We use a straightforward variation on a recent argument of Hezari and Rivière [8] to obtain
localized L p-estimates for all exponents larger than or equal to the critical exponent pc= 2 …

We consider the problem of proving L^ p L p bounds for eigenfunctions of the Laplacian in
the high frequency limit in the presence of nonpositive curvature and more generally …

We survey recent results related to the concentration of eigenfunctions. We also prove some
new results concerning ball-concentration, as well as showing that eigenfunctions saturating …

Let D be a bounded domain in an n-dimensional Euclidean space ℝ n. Assume that $
$0<\lambda _1\leqslant\lambda _2\leqslant\cdots\leqslant\lambda _k\leqslant\cdots $$ are …

Let M be a compact C^∞-smooth Riemannian manifold of dimension n, n≥3, and let
\varphi_λ=\Delta_M\varphi_λ+λ\varphi_λ=0 denote the Laplace eigenfunction on M …

We obtain L p eigenfunction bounds for the harmonic oscillator H=-Δ+x^2 H=-Δ+ x 2 in R^n
ℝ n and for other related operators, improving earlier results of Thangavelu and of …

For small range of p> 2, we improve the L p bounds of eigenfunctions of the Laplacian on
negatively curved manifolds. Our improvement is by a power of logarithm for a full density …

We prove an analogue of Sogge's local L p estimates for L p norms of restrictions of
eigenfunctions to submanifolds, and use it to show that for quantum ergodic eigenfunctions …

Let Δ M be the Laplace operator on a compact n-dimensional Riemannian manifold without
boundary. We study the zero sets of its eigenfunctions u: Δ M u+ λu= 0. In dimension n= 2 we …

We characterize the defect measures of sequences of Laplace eigenfunctions with maximal
L∞ growth. As a consequence, we obtain new proofs of results on the geometry of manifolds …