https://neckpinch.com/authors/eric-chen/New arXiv papers by Eric Chen, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2608.26619arxiv:2608.26619Thu, 27 Aug 2026 00:00:00 GMTKyeongho Bang, Eric Chen, Wenkui Du — We establish the existence and uniqueness modulo time-independent diffeomorphisms of the positively curved ancient Ricci flow (M², ∂M², g(t)) on a two-dimensional surface with boundary, assuming uniformly bounded diameter and constant positive boundary geodesic curvature. In particular, this ancient Ricci flow is rotationally symmetric, its backward limit is the flat disk, and its forward limit is a half-spherical singularity. To our knowledge, this result is the first instance of a classification result for ancient Ricci flows with boundary.Ricci flowAncient solutionsSingularitiesSurfacesStability & uniquenessRotational symmetry & warped products https://arxiv.org/abs/2603.25082arxiv:2603.25082Thu, 26 Mar 2026 00:00:00 GMTRichard H. Bamler, Eric Chen, Ronan J. Conlon — We construct an example of an asymptotically conical (AC) non-Kähler expanding gradient Ricci soliton that has a Kähler tangent cone at infinity. This yields an example of a Kähler cone that can be desingularised by a smooth AC expanding gradient Ricci soliton but not by a smooth AC expanding gradient Kähler–Ricci soliton.Ricci solitonsKähler–Ricci solitonsKähler geometryBoundaries & non-compact https://arxiv.org/abs/2207.07003arxiv:2207.07003Thu, 14 Jul 2022 00:00:00 GMTGilles Carron, Eric Chen, Yi Wang — We study the Yamabe flow on asymptotically flat manifolds with non-positive Yamabe constant Y≤ 0. Previous work by the second and third named authors showed that while the Yamabe flow always converges in a global weighted sense when Y>0, the flow must diverge when Y≤ 0. We show here in the Y≤ 0 case however that after suitable rescalings, the Yamabe flow starting from any asymptotically flat manifold must converge to the unique positive function which solves the Yamabe problem on a compactification of the original manifold.Yamabe flowBoundaries & non-compact https://arxiv.org/abs/2203.05107arxiv:2203.05107Thu, 10 Mar 2022 00:00:00 GMTEric Chen, Guofang Wei, Rugang Ye — We employ the Ricci flow to derive a new theorem about Gromov almost flat manifolds, which generalizes and strengthens the celebrated Gromov–Ruh Theorem. In our theorem, the condition diam² |K| ≤ εₙ in the Gromov–Ruh Theorem is replaced by the substantially weaker condition \|Rm\|_(n/2) C_S² ≤ εₙ.Ricci flow https://arxiv.org/abs/2109.08208arxiv:2109.08208Thu, 16 Sep 2021 00:00:00 GMTSun-Yung Alice Chang, Eric Chen — In this paper, on 4-spheres equipped with Riemannian metrics we study some integral conformal invariants, the sign and size of which under Ricci flow characterize the standard 4-sphere. We obtain a conformal gap theorem, and for Yamabe metrics of positive scalar curvature with L² norm of the Weyl tensor of the metric suitably small, we establish the monotonic decay of the L^p norm for certain p>2 of the reduced curvature tensor along the normalized Ricci flow, with the metric converging exponentially to the standard 4-sphere.Ricci flowScalar curvature