https://neckpinch.com/authors/ronggang-li/New arXiv papers by Ronggang Li, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2609.19851/arxiv:2609.19851Thu, 17 Sep 2026 00:00:00 GMTJian Ge, Chuanhuan Li, Ronggang Li — Let (Mⁿ, g) be a complete, simply connected Riemannian manifold without boundary, of dimension n≥3, with curvature operator at least that of the unit sphere. We prove that ∫_M rm scal(x) d rm Volₓ≤ n(n-1)ωₙ, where ωₙ is the volume of the unit n-sphere. Equality holds if and only if (M,g) is isometric to the unit round sphere. In fact, we obtain a stronger bound containing rm Vol(M, g). In even dimensions, the proof follows from the Chern-Gauss-Bonnet formula. In odd dimensions, we apply the corresponding boundary formula to Deruelle's Ricci expander filling.Ricci solitonsScalar curvature