{"id":"openai-math/Path-selection-and-an-elliptic-inequality-on-degenerating-Ricci-flat-trees","pdf":"https://github.com/openai/math/blob/main/preprints/Path-selection-and-an-elliptic-inequality-on-degenerating-Ricci-flat-trees-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Path-selection-and-an-elliptic-inequality-on-degenerating-Ricci-flat-trees-September-24-2026","tags":["differential-geometry","ricci-flat","elliptic-pde"],"score":0,"title":"Path selection and an elliptic inequality on degenerating Ricci-flat trees","domain":"Differential geometry","family":"351","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DG","summary":"We prove a sequential elliptic inequality for the renormalized Einstein–Hilbert functional on a fixed finite tree of four-dimensional Ricci-flat spaces. As the joining lengths diverge and the scale-neutral weighted Ricci error M tends to zero, the functional satisfies $`E=o(M)`$. The root end has decay exponent greater than one, and every joined quotient group is nontrivial. We also prove the multivariable path-selection theorem for asymptotic expansions used to obtain this estimate.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Scalar curvature and finite-time Ricci-flow singularities"}