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Mathematics > Analysis of PDEs
Title: Nonexistence of invariant nodal line and improved $L^2$ restriction bounds for Neumann data on negatively curved surface
(Submitted on 28 Mar 2024 (v1), last revised 2 Apr 2024 (this version, v2))
Abstract: The problem of obtaining the lower bounds on the restriction of Laplacian eigenfunctions to hypersurfaces inside a compact Riemannian manifold $(M,g)$ is challenging and has been attempted by many authors \cite{BR, GRS, Jun, ET}. This paper aims to show that if $(M,g)$ is assumed to be a negatively curved surface then one can get the corresponding restricted lower bounds, as well as quantitative improvement of restricted bounds for Neumann data.
Submission history
From: Xianchao Wu [view email][v1] Thu, 28 Mar 2024 07:32:29 GMT (23kb)
[v2] Tue, 2 Apr 2024 14:59:02 GMT (0kb,I)
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