https://neckpinch.com/authors/henry-shin/New arXiv papers by Henry Shin, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2608.08533/arxiv:2608.08533Sun, 09 Aug 2026 00:00:00 GMTHenry Shin — We prove that the Feldman–Ilmanen–Knopf (FIK) blowdown singularity has a nonempty open nonlinear formation basin in the full space of smooth Riemannian metrics and, on a smaller neighborhood, local marked first-order asymptotic moduli. Given a closed connected oriented Riemannian four-manifold, an implantation point, and a positive time bound, its oriented blow-up admits a relatively C^(2,α)-open set of smooth metrics whose Ricci flows form, before that time, a localized FIK singularity with global Type-I curvature control. No symmetry, Kähler condition, or finite-dimensional tuning is imposed. Curvature stays uniformly bounded outside the implantation region; fixed-convention marked rescalings converge along the full singular-time sequence to the ancient FIK flow; and the exceptional sphere has sharp FIK asymptotics for area, intrinsic diameter, and curvature. To our knowledge, this is the first open full-metric formation theorem for a finite-time singularity modeled on a noncompact, noncylindrical shrinker. A self-contained spectral certification identifies the weighted FIK operator's nine-dimensional nonnegative space with the scaling and diffeomorphism directions, and exact modulation removes this block. On a smaller little-Hölder h^(2,α) neighborhood, a fixed positive-time restart yields the marked first-profile coordinate A₁=λ_∞^(−γ₁)V_∞∈ E₁. This amplitude is a split C¹ submersion and locally the projection onto E₁. Equality of amplitudes characterizes marked first-order agreement; a transverse disk uniquely realizes each sufficiently small amplitude; normalized two-flow differences converge to the corresponding Jacobi field; and the amplitude determines the first quadratic scale and phase response. This gives a complete local marked first-order profile coordinate for FIK blowdown.Ricci flowRicci solitonsAncient solutionsSingularities4-manifoldsKähler geometryBoundaries & non-compactEigenvalues & spectrum https://neckpinch.com/papers/2505.03823/arxiv:2505.03823Sat, 03 May 2025 00:00:00 GMTBennett Chow, Michael H. Freedman, Henry Shin, Yongjia Zhang — This note corrects an error in the proof of Proposition 13 in arXiv:1903.09181 and simultaneously establishes a more general result. We prove that if M is a compact connected oriented 4-manifold with connected boundary ∂M, and if an unbounded number of disjoint copies of M embed topologically and locally flatly in the interior of a compact 4-manifold N, then TorH₁(∂M;ℤ) is a direct double, i.e., TorH₁(∂M;ℤ)≅ A ⊕ A, with the linking pairing vanishing identically on the first summand, i.e., the linking pairing is split metabolic. This partially generalizes Hantzsche's theorem stating that the linking pairing for a closed 3-manifold that embeds in S⁴ is hyperbolic.Ricci solitonsSingularities4-manifolds