https://neckpinch.com/authors/dongwoo-gang/New arXiv papers by Dongwoo Gang, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2608.14039/arxiv:2608.14039Fri, 14 Aug 2026 00:00:00 GMTDongwoo Gang — For a closed connected Riemannian manifold (M,g), the Gigli–Mantegazza construction pulls back the quadratic Wasserstein metric under the heat kernel embedding x↦ pₜ(x,·) dvol_g. The resulting family gₜ agrees with Ricci flow to first order in t, but in general not to second order. We prove that gₜ =g-2tRic_g +t²(−ΔRic_g +2Ric_g²−2/3𝓠_g) +O_(C⁰)(t³), where 𝓠_g is quadratic in the full curvature tensor. The term −ΔRic_g also occurs in the second-order expansion of Ricci flow, so the discrepancy depends pointwise and quadratically on the curvature. In particular, at a Ricci-flat metric that is not flat, Ricci flow is stationary while gₜ is not. The Gromov–Hausdorff distance between the Gigli–Mantegazza and Ricci-flow metrics is O(t²), and round spheres show that this estimate is sharp.Ricci flowRicci-flat & Calabi–YauHeat kernelLimit spaces & RCD