Convexity estimates for level sets of quasiconcave solutions to fully nonlinear elliptic equations
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Bibliographic record
Abstract
We establish a global geometric lower bound for the second fundamental form of the level surfaces of solutions to F(D2u, Du, u, x) = 0 in convex ring domains, in terms of boundary geometry and the structure of the elliptic operator F. We also prove a microscopic constant rank theorem, under a general structural condition introduced by Bianchini–Longinetti–Salani in 2009.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
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