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We extend a result of the second author [27, Theorem 1.1] to dimensions $d \geq 3$ which relates the size of $L^{p}$ -norms of eigenfunctions for $2 < p < 2 (d + 1) / d - 1$ to the amount of $L^{2}$ -mass in shrinking tubes about unit-length geodesics. The proof uses bilinear oscillatory integral estimates of Lee [22] and a variable coefficient variant of an " $ϵ$ removal lemma" of Tao and Vargas [35]. We also use Hörmander’s [20] $L^{2}$ oscillatory integral theorem and the Cartan–Hadamard theorem to show that, under the assumption of nonpositive curvature,...

Strichartz estimates for the wave equation on manifolds with boundary

Matthew D. Blair; Hart F. Smith; Christopher D. Sogge — 2009

Annales de l'I.H.P. Analyse non linéaire

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Propagation of singularities and maximal functions in the plane.

$L^{p}$ estimates for the wave equation and applications

Riemannian manifolds with maximal eigenfunction growth

Oscillatory integrals associated to folding canonical relations

Null form estimates for $(1 / 2, 1 / 2)$ symbols and local existence for a quasilinear dirichlet-wave equation

On Kakeya–Nikodym averages, $L^{p}$ -norms and lower bounds for nodal sets of eigenfunctions in higher dimensions

Strichartz estimates for the wave equation on manifolds with boundary

Advanced Search

Formula preview

Currently displaying 1 – 7 of 7

Propagation of singularities and maximal functions in the plane.

L p estimates for the wave equation and applications

Riemannian manifolds with maximal eigenfunction growth

Oscillatory integrals associated to folding canonical relations

Null form estimates for ( 1 / 2 , 1 / 2 ) symbols and local existence for a quasilinear dirichlet-wave equation

On Kakeya–Nikodym averages, L p -norms and lower bounds for nodal sets of eigenfunctions in higher dimensions

Strichartz estimates for the wave equation on manifolds with boundary

$L^{p}$ estimates for the wave equation and applications

Null form estimates for $(1 / 2, 1 / 2)$ symbols and local existence for a quasilinear dirichlet-wave equation

On Kakeya–Nikodym averages, $L^{p}$ -norms and lower bounds for nodal sets of eigenfunctions in higher dimensions