Propagation of singularities and maximal functions in the plane.
estimates for the wave equation and applications
Riemannian manifolds with maximal eigenfunction growth
Oscillatory integrals associated to folding canonical relations
Null form estimates for symbols and local existence for a quasilinear dirichlet-wave equation
On Kakeya–Nikodym averages, -norms and lower bounds for nodal sets of eigenfunctions in higher dimensions
We extend a result of the second author [27, Theorem 1.1] to dimensions which relates the size of -norms of eigenfunctions for to the amount of -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 " removal lemma" of Tao and Vargas [35]. We also use Hörmander’s [20] 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
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