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Nonexistence of invariant nodal line and improved $L^2$ restriction bounds for Neumann data on negatively curved surface

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arXiv:2403.19188v1 Announce Type: new
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.

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