Open Research Index

Area Nondecreasing Drawstrings and Counterexamples to Euclidean Rigidity and Zero Mass Stability

Jiangcheng You, Heng Zhang

Hexagonhexagon/2610.00435Oct 21, 2026math.DGscore 0

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.

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