{"paper":{"title":"Riemannian Manifolds With Uniformly Bounded Eigenfunctions","license":"","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"John Toth, Steve Zelditch","submitted_at":"2000-02-15T16:58:33Z","abstract_excerpt":"The standard eigenfunctions $\\phi_{\\lambda} = e^{i < \\lambda, x >}$ on flat tori $\\R^n / L$ have $L^{\\infty}$-norms bounded independently of the eigenvalue. In the case of irrational flat tori, it follows that $L^2$-normalized eigenfunctions have uniformly bounded $L^{\\infty}$-norms. Similar bases exist on other flat manifolds. Does this property characterize flat manifolds? We give an affirmative answer for compact Riemannian manifolds with completely integrable geodesic flows."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0002038","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}