Year: 2024
Type: preprint
Abstract: Let $\{u_λ\}$ be a sequence of $L^2$-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} \partial_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 $O(λ^{-\frac{1}p+\frac{3}2})$. The Van De Corput theorem (Lemma 2.1) plays the crucial role in our proof. Moreover, this upper bound is shown to be optimal.
Source: arXiv (Cornell University)
Author: Wu, Xianchao
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4393213303