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 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 prove a generalized version of the Quantum Ergodicity Theorem on smooth compact
Riemannian manifolds without boundary. We apply it to prove some asymptotic properties …

We give an overview of some old results on weak* limits of eigenfunctions and prove some
new ones. We first show that on M=(S n, can) every probability measure on S* M which is …

Norms and Quantum Ergodicity on the Sphere Jeffrey M. VanderKam Page 1 IMRN International
Mathematics Research Notices 1997, No. 7 L ∞ Norms and Quantum Ergodicity on the Sphere …

This is a survey of recent results on quantum ergodicity, specifically on the large energy
limits of matrix elements relative to eigenfunctions of the Laplacian. It is mainly devoted to …

Let M be a smooth closed Riemannian manifold and∆ the Laplace operator. A function u is
said to be an eigenfunction with eigenvalue λ if∆ u=− λu.(0.1) With our convention on the …

We prove lower bounds for the entropy of limit measures associated to non-degenerate
sequences of eigenfunctions on locally symmetric spaces of non-positive curvature. In the …

We prove that, for an n-dimensional compact Riemannian manifold (M, g), the (n− 1)-
dimensional Hausdorff measure| Z λ| of the zero-set Z λ of an eigenfunction e λ of the …

In this paper, we investigate quantum ergodicity in negatively curved manifolds. We consider
the symbols depending on a semiclassical parameter h with support shrinking down to a …