A <i>C</i> <sup>0</sup> -estimate for the parabolic Monge–Ampère equation on complete non-compact Kähler manifolds
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Abstract In this article we study the Kähler–Ricci flow, the corresponding parabolic Monge–Ampère equation and complete non-compact Kähler–Ricci flat manifolds. Our main result states that if ( M , g ) is sufficiently close to being Kähler–Ricci flat in a suitable sense, then the Kähler–Ricci flow has a long time smooth solution g ( t ) converging smoothly uniformly on compact sets to a complete Kähler–Ricci flat metric on M . The main step is to obtain a uniform C 0 -estimate for the corresponding parabolic Monge–Ampère equation. Our results on this can be viewed as parabolic versions of the main results of Tian and Yau [ Complete Kähler manifolds with zero Ricci curvature. II , Invent. Math. 106 (1990), 27–60] on the elliptic Monge–Ampère equation.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it