https://neckpinch.com/authors/yuxing-deng/New arXiv papers by Yuxing Deng, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2603.28014arxiv:2603.28014Mon, 30 Mar 2026 00:00:00 GMTYuxing Deng, Ganqi Wang, Yongjia Zhang — In this paper, we study the asymptotic geometry of a noncollapsed ancient Ricci flow with nonnegative Ricci curvature via its tangent flow at infinity – a noncollapsed F-limit metric soliton [Bam23,CMZ23]. We first prove some estimates for noncollapsed F-limit metric solitons with nonnegative Ricci curvature, and then obtain two dichotomy theorems for ancient Ricci flows. In particular, we show that: (1) for a noncollapsed ancient Ricci flow with nonnegative Ricci curvature, either its asymptotic volume ratio is always zero, or every tangent flow at infinity is a Ricci flat cone; (2) for a noncollapsed ancient Ricci flow with positively pinched Ricci curvature (Ric≥ εR g), either it is compact, or every tangent flow at infinity is a Ricci flat cone.Ricci flowAncient solutionsRicci-flat & Calabi–YauSingularities(Non)collapsing https://arxiv.org/abs/2504.14525arxiv:2504.14525Sun, 20 Apr 2025 00:00:00 GMTYuxing Deng — In this paper, we study gradient Ricci soitons on smooth orbifolds. We prove that the scalar curvature of a complete shrinking or steady gradient Ricci soliton on an orbifold is nonnegative. We also show that a complete κ-noncollapsed steady gradient Ricci soliton on a Riemannian orbifold with positive curvature operator, compact singularity and linear curvature decay must be a finite quotient of the Bryant soliton. Finally, we show that a complete steady gradient Ricci soliton on a Riemannian orbifold with positive sectional curvature must be a finite quotient of the Bryant soliton if it is asymptotically quotient cylindrical.Ricci solitonsAncient solutionsSingularities(Non)collapsingSphere theoremsScalar curvatureStability & uniqueness https://arxiv.org/abs/2412.07452arxiv:2412.07452Tue, 10 Dec 2024 00:00:00 GMTYuxing Deng, Yuehan Hao — In this paper, we study the fundamental group of the complete steady gradient Ricci soliton with nonnegative sectional curvature. We prove that the fundamental group of such a Ricci soliton is either trivial or infinite. As a corollary, we show that an n-dimensional complete κ-noncollapsed steady gradient Ricci soliton with nonnegative sectional curvature must be diffeomorphic to ℝⁿ.Ricci solitons(Non)collapsing