The L^p restriction bounds for Neumann data on surface

2024/03/25 by Wu, Xianchao
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.16445

Abstract

Let \u_λ\ be a sequence of L²-normalized Laplacian eigenfunctions on a compact two-dimensional smooth Riemanniann manifold (M,g). We seek to get an L^p restriction bounds of the Neumann data λ^-1 ∂_νu_λ \vline_γ along a unit geodesic γ. Using the T-T^* argument one can transfer the problem to an estimate of the norm of a Fourier integral operator and show that such bound is O(λ^-\frac1p+\frac32). The Van De Corput theorem (Lemma 2.1) plays the crucial role in our proof. Moreover, this upper bound is shown to be optimal.

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