https://neckpinch.com/authors/hong-huang/New arXiv papers by Hong Huang, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2311.15825arxiv:2311.15825Mon, 27 Nov 2023 00:00:00 GMTHong Huang — We prove the following result: Let (M,g₀) be a complete noncompact manifold of dimension n≥ 12 with isotropic curvature bounded below by a positive constant, with scalar curvature bounded above, and with injectivity radius bounded below. Then there is a finite collection 𝓧 of spherical n-manifolds and manifolds of the form Sⁿ⁻¹ × ℝ /G, where G is a discrete subgroup of the isometry group of the round cylinder Sⁿ⁻¹× ℝ, such that M is diffeomorphic to a (possible infinite) connected sum of members of 𝓧. This extends a recent work of Huang. The proof uses Ricci flow with surgery on open orbifolds with isolated singularities.Ricci flowSingularitiesSurgerySphere theoremsScalar curvatureBoundaries & non-compact https://arxiv.org/abs/2305.18154arxiv:2305.18154Mon, 29 May 2023 00:00:00 GMTHong Huang — We show the following result: Let (M,g₀) be a compact manifold of dimension n≥ 12 with positive isotropic curvature. Then M is diffeomorphic to a spherical space form, or a quotient manifold of Sⁿ⁻¹× ℝ by a cocompact discrete subgroup of the isometry group of the round cylinder Sⁿ⁻¹× ℝ, or a connected sum of a finite number of such manifolds. This extends previous works of Brendle and Chen-Tang-Zhu, and improves a work of Huang. The proof uses Ricci flow with surgery on compact orbifolds, with the help of the ambient isotopy uniqueness of closed tubular neighborhoods of an isolated singular point in an orbifold.Ricci flowSurgerySphere theoremsStability & uniqueness https://arxiv.org/abs/2108.04761arxiv:2108.04761Tue, 10 Aug 2021 00:00:00 GMTHong Huang — In this short note we obtain some local and global upper bounds for the Hessian of a positive solution to the conjugate heat equation coupled with the Ricci flow.Ricci flowHeat kernel