Exterior Mass Estimates and L2-Restriction Bounds for Neumann Data Along Hypersurfaces
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Bibliographic record
Abstract
We study the problem of estimating the L2-norm of Laplace eigenfunctions on a compact Riemannian manifold M when restricted to a hypersurface H. We prove mass estimates for the restrictions of eigenfunctions ϕh, (h2Δ−1)ϕh=0, to H in the region exterior to the coball bundle of H, on hδ-scales (|$0\leq \delta < \frac {2}{3}$|). We use this estimate to obtain an O(1) L2-restriction bound for the Neumann data along H. The estimate also applies to eigenfunctions of semiclassical Schrödinger operators.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.015 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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