{"id":"hexagon/2610.00435","pdf":"https://hexagonmath.org/pdf/2610.00435v1","url":"https://hexagonmath.org/abs/2610.00435v1","tags":["msc:53C24","msc:53C21","msc:53C23","ADM mass","AF manifolds","Drawstring constructions","Gromov's Euclidean C^0 rigidity conjecture","Intrinsic flat convergence","Positive mass theorem","Scalar curvature rigidity"],"score":0,"title":"Area Nondecreasing Drawstrings and Counterexamples to Euclidean Rigidity and Zero Mass Stability","domain":"math.DG","source":"hexagon","authors":["Jiangcheng You","Heng Zhang"],"reviews":0,"subject":"math.DG","summary":"Building on the drawstring construction of Kazaras--Xu, we develop a localized refinement that contracts prescribed curves while preserving positive scalar curvature and without decreasing two-dimensional area. As two applications, we disprove part~(b) of Gromov's Euclidean $C^0$ rigidity conjecture and Sormani's zero mass stability conjecture.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT"],"discussed":0,"published":"2026-10-21","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}