Improved critical eigenfunction restriction estimates on Riemannian surfaces with nonpositive curvature

DOI10.1007/s00220-016-2721-9zbMath1360.58024arXiv1603.01601OpenAlexW3099667105WikidataQ115388566 ScholiaQ115388566MaRDI QIDQ514331

Cheng Zhang, Yakun Xi

Publication date: 1 March 2017

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.01601

zbMATH Keywords

logarithmic estimates\(L^4\) restriction estimatesnon-positive scalar curvatureoscillatory integral estimatesToponogov's theorem

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Harmonic functions on Riemann surfaces (30F15)

Related Items (7)

On logarithmic improvements of critical geodesic restriction bounds in the presence of nonpositive curvature ⋮ Quantum entanglement and the growth of Laplacian eigenfunctions ⋮ Eigenfunction restriction estimates for curves with nonvanishing geodesic curvatures in compact Riemannian surfaces with nonpositive curvature ⋮ Quantum ergodicity and \(L^{p}\) norms of restrictions of eigenfunctions ⋮ Restriction of toral eigenfunctions to totally geodesic submanifolds ⋮ Sharp endpoint estimates for eigenfunctions restricted to submanifolds of codimension 2 ⋮ Inner product of eigenfunctions over curves and generalized periods for compact Riemannian surfaces

Cites Work

• Unnamed Item
• Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds
• Concerning the \(L^ p\) norm of spectral clusters for second-order elliptic operators on compact manifolds
• Besicovitch type maximal operators and applications to Fourier analysis
• On the wave equation on a compact Riemannian manifold without conjugate points
• Improved critical eigenfunction estimates on manifolds of nonpositive curvature
• Concerning Toponogov's theorem and logarithmic improvement of estimates of eigenfunctions
• A few endpoint geodesic restriction estimates for eigenfunctions
• Improvement of eigenfunction estimates on manifolds of nonpositive curvature
• Extensions of the Stein-Tomas theorem
• On eigenfunction restriction estimates and $L^4$-bounds for compact surfaces with nonpositive curvature
• Lp norm estimates of eigenfunctions restricted to submanifolds
• An improvement on eigenfunction restriction estimates for compact boundaryless Riemannian manifolds with nonpositive sectional curvature
• Hangzhou Lectures on Eigenfunctions of the Laplacian

This page was built for publication: Improved critical eigenfunction restriction estimates on Riemannian surfaces with nonpositive curvature