Related papers: A uniqueness theorem for asymptotically cylindrica…

We consider noncollapsed steady gradient Ricci solitons with nonnegative sectional curvature. We show that such solitons always dimension reduce at infinity. This generalizes an earlier result in [CDM22] to higher dimensions. In dimension…

We construct an expanding gradient Ricci soliton in dimension three over the topological manifold R x T^2 (the product of a line and a torus) that aproaches asymptotically a constant curvature cusp at one end, and a flat manifold on the…

We establish the short-time existence of the Ricci flow on surfaces with a finite number of conic points, all with cone angle between 0 and $2\pi$, where the cone angles remain fixed or change in some smooth prescribed way. For the…

We prove the following rigidity theorem: For an n-dimensional compact Riemannian manifold with boundary whose Ricci curvature is bounded by n-1 from below, if its boundary is isometric to the standard sphere of dimension n-1 and totally…

We prove that there exists a gradient expanding Ricci soliton asymptotic to any given cone over the product of a round sphere and a Ricci flat manifold. In particular we obtain asymptotically conical expanding Ricci solitons with positive…

In this article we classify expanding homogeneous Ricci solitons up to dimension 5, according to their presentation as homogeneous spaces. We obtain that they are all isometric to solvsolitons, and this in particular implies that the…

In this note we prove that any four-dimensional half conformally flat gradient steady Ricci soliton must be either Bryant's soliton or Ricci flat. We also classify four-dimensional half conformally flat gradient shrinking Ricci solitons…

This work addresses the questions: (i) Among all left-invariant Riemannian metrics on a given Lie group, is there any whose isometry group or isometry algebra contain that of all others? (ii) Do expanding left-invariant Ricci solitons…

We establish sufficient conditions which ensure that a locally-warped product structure propagates backward in time under the Ricci flow. As an application, we prove that if an asymptotically conical gradient shrinking soliton is asymptotic…

We first show that a K\"ahler cone appears as the tangent cone of a complete expanding gradient K\"ahler-Ricci soliton with quadratic curvature decay with derivatives if and only if it has a smooth canonical model (on which the soliton…

We use the theory of isoparametric functions to investigate gradient Ricci solitons with constant scalar curvature. We show rigidity of gradient Ricci solitons with constant scalar curvature under some conditions on the Ricci tensor, which…

We prove that any shrinking Kahler Ricci soliton has only one end, and that any expanding Kahler Ricci soliton with proper potential has only one end.

We discuss some geometric conditions under which a complete noncompact shrinking gradient Ricci soliton will split at infinity.

In this paper, we classify n-dimensional (n>3) complete Bach-flat gradient shrinking Ricci solitons. More precisely, we prove that any 4-dimensional Bach-flat gradient shrinking Ricci soliton is either Einstein, or locally conformally flat…

In this paper, we study the following conjecture of Hamilton: Any compact gradient shrinking Ricci soliton with positive curvature operator must be Einstein. We first derive several identities. Then we show that the conjecture is true under…

In this paper we consider the Ricci curvature of a Ricci soliton. In particular, we have showed that a complete gradient Ricci soliton with non-negative Ricci curvature possessing a non-constant convex potential function having finite…

In this paper, we prove the uniqueness of K\"ahler Ricci shrinkers on toric orbifolds, extending the corresponding results previously established for toric manifolds.

We study the modified Ricci solitons as a new class of Einstein type metrics that contains both Ricci solitons and $n$-quasi-Einstein metrics. This class is closely related to the construction of the Ricci solitons that are realised as…

We show that $\kappa$-solutions to the Ricci flow in dimensions $n\geq 4$ whose asymptotic shrinking Ricci soliton is the round cylinder $\mathbb{S}^{n-1}\times\mathbb{R}$ must be uniformly PIC. Combined with earlier classification results,…

We study the asymptotic volume ratio of non-steady gradient Ricci solitons. Moreover, a local estimate of the volume ratio is obtained for expanding solitons which satisfy $\lim_{dist(O,x)\rightarrow\infty} |Sect|\cdot dist(O,x)^2=0$.…