arXiv research

Extends soliton theory to non-compact cases.

Study on transverse Ricci solitons on compact foliated manifolds.

Paper shows k-Yamabe solitons have constant curvature under certain conditions.

We prove some results for the solitons of the Ricci-Bourguignon flow, generalizing corresponding results for Ricci solitons. Taking motivation from Ricci almost solitons, we then introduce the notion of Ricci-Bourguignon $almost$ solitons and prove some results about them which generalize previous results for Ricci alm…

The study proves triviality and rigidity results for Ricci solitons and estimates their conjugate radius.

Compact gradient ρ-Einstein solitons are isometric to Euclidean spheres.

Study on 4D compact Ricci solitons and their geometric properties.

Paper shows constant σk-curvature for quasi k-Yamabe solitons.

The paper studies integral formulas for a specific type of soliton.

Study clarifies almost Ricci-Bourguignon solitons and their properties.

The paper examines conditions for a vector field to be Killing in almost Yamabe solitons.

The study examines 4D steady gradient Ricci solitons with nonnegative curvature away from a compact set.

Study stability of compact Ricci solitons using entropy variations.

It is shown that the diameter of a compact shrinking Ricci soliton has a universal lower bound. This is proved by extending universal estimates for the first non-zero eigenvalue of Laplacian on compact Riemannian manifolds with lower Ricci curvature bound to a twisted Laplacian on compact shrinking Ricci solitons.

Paper proves rigidity for Ricci solitons with specific conditions.

Ricci solitons on Finsler spaces, previously developed by the present authors, are a generalization of Einstein spaces, which can be considered as a solution to the Ricci flow on compact Finsler manifolds. In the present work it is shown that on a Finslerian space, a forward complete shrinking Ricci soliton is compact …

Undergraduate thesis explores topological barriers to compact Ricci solitons in 4D.

Conditions for trivial gradient hyperbolic Ricci and Yamabe solitons to be Einstein or constant scalar curvature.

In this paper we prove the compactness result for compact Kähler Ricci gradient shrinking solitons. If $(M_i,g_i)$ is a sequence of Kähler Ricci solitons of real dimension $n \ge 4$, whose curvatures have uniformly bounded $L^{n/2}$ norms, whose Ricci curvatures are uniformly bounded from below and $μ(g_i,1/2) \ge A$ (…

Sharp upper diameter limit found for Ricci solitons.

Researchers find limits on curvature of certain 3D solitons.

Paper examines conditions making Riemann solitons trivial and estimates their scalar curvature.

In this paper, we give a delay estimate of scalar curvature for a complete non-compact expanding (or steady) gradient Ricci soliton with nonnegative Ricci curvature. As an application, we prove that any complete non-compact expanding (or steady) gradient Kähler-Ricci solitons with positively pinched Ricci curvature sho…

Unique shrinking gradient Kähler-Ricci solitons found on non-compact toric manifolds.

In this paper, we prove the compactness theorem for gradient Ricci solitons. Let $(M_α, g_α)$ be a sequence of compact gradient Ricci solitons of dimension $n\geq 4$, whose curvatures have uniformly bounded $L^{\frac{n}{2}}$ norms, whose Ricci curvatures are uniformly bounded from below with uniformly lower bounded vol…

In this paper, we show that the Webster scalar curvature of any compact CR Yamabe soliton must be constant.

In this article, stimulated by Fernandez-Lopez and Garcia-Rio, we shall give an upper diameter bound for compact Ricci solitons in terms of the range of the scalar curvature. As an application, we shall provide some sufficient conditions for four-dimensional compact Ricci solitons to satisfy the Hitchin-Thorpe inequali…

The study finds a lower bound for the diameter of gradient ρ-Einstein solitons.

We study the stability of non compact steady and expanding gradient Ricci solitons. We first show that strict linear stability implies dynamical stability. Then we give various sufficient geometric conditions ensuring the strict linear stability of such gradient Ricci solitons.

The study characterizes quasi Yamabe solitons with potential vector fields.

We show that sequences of compact gradient Ricci solitons converge to complete orbifold gradient solitons, assuming constraints on volume, the $L^{n/2}$-norm of curvature, and the auxiliary constant $C_1$. The strongest results are in dimension 4, where $L^2$ curvature bounds are equivalent to upper bounds on the Euler…

We first investigate the asymptotics of conical expanding gradient Ricci solitons by proving sharp decay rates to the asymptotic cone both in the generic and the asymptotically Ricci flat case. We then establish a compactness theorem concerning nonnegatively curved expanding gradient Ricci solitons.

Compact Ricci solitons on surfaces have at most two cone points, and are known as Hamilton's footballs. In this note we completely describe the degenerations of these footballs as one or both of the cone angles approaches zero. In particular, we show that Hamilton's famous non-compact cigar soliton is the Gromov--Hausd…

Study on gradient h-almost Yamabe solitons with scalar curvature estimation.

The paper examines the geometry and topology of Sasaki-Ricci solitons, proving they are either connected at infinity or compact.

Study classifies bubbles of Type I singularities in Kähler-Ricci flow on compact surfaces.

Ancient Ricci flows on compact spaces converge to solitons.

In $N(k)$-contact metric manifolds and/or $(k,μ)$-manifolds, gradient Ricci solitons, compact Ricci solitons and Ricci solitons with $V$ pointwise collinear with the structure vector field $ξ$ are studied.

The paper characterizes rigidity in harmonic-Ricci solitons.

By extending Koiso's examples to the non-compact case, we construct complete gradient Kahler-Ricci solitons of various types on certain holomorphic line bundles over compact Kahler-Einstein manifolds. Moreover, a uniformization result on steady gradient Kahler-Ricci solitons with non-negative Ricci curvature is obtaine…

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 an additional condition. Furthermore, such a soliton must be of constant curvat…

The aim of this article is to study the k-almost Ricci soliton and k-almost gradient Ricci soliton on contact metric manifold. First, we prove that if a compact K-contact metric is a k-almost gradient Ricci soliton then it is isometric to a unit sphere S2n+1. Next, we extend this result on a compact k-almost Ricci soli…

Study on geometric properties of second Ricci solitons.

Study of generalized almost-Kähler-Ricci solitons and their implications.

Study on shrinking solitons of generalized Ricci flow.

Study 4D steady gradient Ricci solitons reducing to 3D manifolds.

Study on 4D solitons with curvature constraints.

Classifies Ricci soliton subgroups in specific Lie groups.