{"id":"openai-math/Sharp-integral-fillings-in-CAT(0)-spaces","pdf":"https://github.com/openai/math/blob/main/preprints/Sharp-integral-fillings-in-CAT(0)-spaces-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Sharp-integral-fillings-in-CAT(0)-spaces-September-23-2026","tags":["geometric-measure-theory","isoperimetry","cat0-spaces"],"score":0,"title":"Sharp integral fillings in CAT(0) spaces","domain":"Differential geometry","family":"337","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DG","summary":"Every compactly supported integral n -cycle, n ≥ 2, in a proper CAT(0) space bounds a compactly supported integral current with the sharp Euclidean mass bound. The theorem allows arbitrary integer multiplicities and unrestricted ambient dimension. In particular, we prove the Euclidean Cartan–Hadamard isoperimetric conjecture in dimensions at least three.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Sharp Cartan–Hadamard isoperimetry and rigidity"}