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[Ary26] Shrey Aryan,Spectral obstructions to contracting transport maps on curved spaces (2026)

[AN54] Yasuo Akizuki, Shigeo Nakano,Note on Kodaira–Spencer’s proof of Lefschetz theorems, Proceedings of the Japan Academy30( · 1954 · Proceedings of the Japan Academy Series A Mathematical Sciences · DOI 10.3792/pja/1195526105 · arXiv pja/1195526

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Eigenvalues on spheres

math.DG · 2026-07-13 · accept · novelty 8.0

Curvature ≥1 on S^{2} forces ordered Laplace eigenvalues and finite spectral counts to dominate the round sphere, with equality rigidity, implying sharp dim H_d ≤ (d+1)^{2} on 3-manifolds with K≥0 and AVR>0.

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  • Eigenvalues on spheres math.DG · 2026-07-13 · accept · none · ref 1

    Curvature ≥1 on S^{2} forces ordered Laplace eigenvalues and finite spectral counts to dominate the round sphere, with equality rigidity, implying sharp dim H_d ≤ (d+1)^{2} on 3-manifolds with K≥0 and AVR>0.