https://neckpinch.com/authors/matthew-gursky/New arXiv papers by Matthew Gursky, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1809.05918/arxiv:1809.05918Sun, 16 Sep 2018 00:00:00 GMTSun-Yung A. Chang, Matthew Gursky, Siyi Zhang — We extend the sphere theorem of to give a conformally invariant characterization of (ℂP}², g_FS). In particular, we introduce a conformal invariant β(M⁴,[g]) ≥ 0 defined on conformal four-manifolds satisfying a `positivity' condition; it follows from that if 0 ≤ β(M⁴,[g]) < 4, then M⁴ is diffeomorphic to S⁴. Our main result of this paper is a `gap' result showing that if b₂⁺(M⁴) > 0 and 4 ≤ β(M⁴,[g]) < 4(1 + ε) for ε> 0 small enough, then M⁴ is diffeomorphic to ℂP}². The Ricci flow is used in a crucial way to pass from the bounds on β to pointwise curvature information.Ricci flow4-manifoldsSphere theorems