Restriction of toral eigenfunctions to hypersurfaces
Jean Bourgain, Zeev Rudnick
TL;DR
This paper derives uniform bounds for Laplacian eigenfunctions on flat tori when restricted to curved hypersurfaces, advancing understanding of eigenfunction behavior in geometric analysis.
Contribution
It provides the first uniform bounds on eigenfunction restrictions to curved hypersurfaces on flat tori, filling a gap in spectral geometry.
Findings
Established uniform upper bounds on eigenfunction restrictions.
Established uniform lower bounds on eigenfunction restrictions.
Applicable to 2D and 3D flat tori with curved hypersurfaces.
Abstract
We establish uniform upper and lower bounds on the restrictions of the eigenfunctions of the Laplacian on the 2- and 3-dimensional standard flat torus to smooth hyper-surfaces with non-vanishing curvature.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Analytic and geometric function theory