https://neckpinch.com/authors/jingbo-wan/New arXiv papers by Jingbo Wan, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2608.18002arxiv:2608.18002Tue, 18 Aug 2026 00:00:00 GMTTsz-Kiu Aaron Chow, Jingbo Wan — For m=2,3, we prove that every smooth immersion F:ℝℙ^mlooparrowrightoverline{B^(,N)(1) satisfies κ(F)²≥ 2m/(m+1), with equality only for the Veronese embedding, up to congruence. We also prove that a closed, connected, orientable three-manifold admitting an immersion into a Euclidean unit ball with κ(F)≤√(3/2) is diffeomorphic to S³, ℝℙ³, or S²× S¹. All three possibilities occur, while κ(F)<√(3/2) forces X≅ S³. These results answer a question of Petrunin and prove a conjecture of Chodosh–Li concerning the normal curvature of three-manifolds. The key intrinsic input is the strict scalar–systolic inequality (min_Y R_g)sys(g)²<6π² for every spherical three-space form Y with |π₁(Y)|>2. Its proof uses systolic monotonicity along Ricci flow with surgery. This strict inequality complements the sharp scalar–systolic inequality for ℝℙ³ of Bray–Brendle–Eichmair–Neves.Ricci flowSurgery3-manifoldsSphere theorems https://arxiv.org/abs/2407.05602arxiv:2407.05602Mon, 08 Jul 2024 00:00:00 GMTJingbo Wan — We prove the sharp interior gradient estimate for area decreasing graphical mean curvature flow in arbitrary codimension, which generalizes the result in.Mean curvature flow https://arxiv.org/abs/2312.10940arxiv:2312.10940Mon, 18 Dec 2023 00:00:00 GMTMan-Chun Lee, Luen-Fai Tam, Jingbo Wan — In this work, we consider the area non-increasing map between manifolds with positive curvature. By exploring the strong maximum principle along the graphical mean curvature flow, we show that an area non-increasing map between certain positively curved manifolds is either homotopy trivial, Riemannian submersion, local isometry or isometric immersion. This implies that an area non-increasing self map of ℂP}ⁿ, n≥ 2 is either homotopically trivial or is an isometry. This confirms a speculation of Tsai-Tsui-Wang. We also use Brendle's sphere Theorem and mean curvature flow coupled with Ricci flow to establish related results on manifolds with positive 1-isotropic curvature.Ricci flowMean curvature flowSphere theoremsStability & uniqueness