{"id":"openai-math/Weak-Hessian-bounds-along-every-geodesic-in-RCD-spaces","pdf":"https://github.com/openai/math/blob/main/preprints/Weak-Hessian-bounds-along-every-geodesic-in-RCD-spaces-September-24-2026/weak-hessian-geodesics.pdf","url":"https://github.com/openai/math/tree/main/preprints/Weak-Hessian-bounds-along-every-geodesic-in-RCD-spaces-September-24-2026","tags":["metric-measure-spaces","optimal-transport","rcd-spaces"],"score":0,"title":"Weak Hessian bounds along every geodesic in RCD spaces","domain":"Differential geometry","family":"356","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DG","summary":"On a full-support $`\\mathrm{RCD}(K,N)`$ space with $`1\\lt N\\lt \\infty`$, we prove that a bounded globally Lipschitz function whose distributional Hessian is bounded above by a bounded continuous function satisfies the corresponding second-derivative inequality along every minimizing geodesic.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":true,"family_title":"Gigli’s characterization of Alexandrov curvature"}