On eigenfunction restriction estimates and $L^4$-bounds for compact surfaces with nonpositive curvature

Details On eigenfunction restriction estimates and $L^4$-bounds for compact surfaces with nonpositive curvature On eigenfunction restriction estimates and $L^4$-bounds for compact surfaces with nonpositive curvature

2011-08-12

arxiv.org/abs/1108.2726v2

Mathematics

Analysis of PDEs

11 pages, corrected a copule of typos. Submitted to the proceedings honoring E. M. Stein's 80th birthday

Scientific paper

Let $(M,g)$ be a two-dimensional compact boundaryless Riemannian manifold with nonpostive curvature, then we shall give improved estimates for the $L^2$-norms of the restrictions of eigenfunctions to unit-length geodesics, compared to the general results of Burq, G\'erard and Tzvetkov \cite{burq}. By earlier results of Bourgain \cite{bourgainef} and the first author \cite{Sokakeya}, they are equivalent to improvements of the general $L^p$-estimates in \cite{soggeest} for $n=2$ and $2

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