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 prove new improved endpoint, $ L^{p_c} $, $ p_c=\tfrac {2 (n+ 1)}{n-1} $, estimates (the"
kink point") for eigenfunctions on manifolds of nonpositive curvature. We do this by using …

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 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 …

Let (M, g) be a compact, boundaryless manifold of dimension n with the property that either
(i) n= 2 and (M, g) has no conjugate points, or (ii) the sectional curvatures of (M, g) are …

Let $(M, g) $ be a two-dimensional compact boundaryless Riemannian manifold with
nonpostive curvature, then we shall give improved estimates for the $ L^ 2$-norms of the …

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 …

This thesis covers different aspects of the p-Laplace operators on Riemannian manifolds.
Chapter 2. Potential theoretic aspects: the Khasmkinskii condition. Chapter 3: sharp …

We study the relationship between L∞ growth of eigenfunctions and their L 2 concentration
as measured by defect measures. In particular, we show that scarring in the sense of …

We show that one can obtain improved L 4 geodesic restriction estimates for eigenfunctions
on compact Riemannian surfaces with nonpositive curvature. We achieve this by adapting …