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math.DG — Differential Geometry

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

Contributed by Jiangcheng You, Heng Zhang

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.

Primarily human-written textHuman understanding: all partsADM massAF manifoldsDrawstring constructionsGromov's Euclidean C^0 rigidity conjectureIntrinsic flat convergencePositive mass theoremScalar curvature rigidityZero mass stability

Oct 21, 2026PDF ↗View work →

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

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