https://neckpinch.com/authors/wooseok-shin/New arXiv papers by Wooseok Shin, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2608.25704/arxiv:2608.25704Wed, 26 Aug 2026 00:00:00 GMTJeongHyeong Park, Wooseok Shin — We prove that every compact four-dimensional weakly Einstein Ricci soliton is Einstein. The nontrivial compact case reduces to the gradient shrinking setting, where a differential identity for weakly Einstein four-manifolds, together with the curvature identity for gradient Ricci solitons, yields the pointwise relation |R|²∇f=0 for the soliton potential f. Consequently, no compact proper weakly Einstein four-manifold admits a Ricci soliton structure. A noncompact homogeneous example shows that the compactness assumption is essential.Ricci solitons4-manifoldsLimit spaces & RCDHomogeneous spacesStability & uniquenessBoundaries & non-compact