arXiv research

New expanding Ricci solitons found starting in dimension four.

Paper proves rigidity for Ricci solitons with specific conditions.

Study classifies 4D Ricci solitons with specific curvature conditions.

Sharp curvature estimates for expanding Ricci solitons in various dimensions.

New example of non-Kähler soliton with Kähler-like behavior at infinity.

Paper reviews and proves volume growth estimates for different types of gradient Ricci solitons.

The paper pinches curvature in expanding Ricci solitons.

Constructs expanding gradient Ricci solitons with unique properties.

Unique steady and expanding solitons with spherical links identified.

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.

3D solitons classified into specific types.

Unique continuation result for expanding Ricci solitons.

Study cohomogeneity one expanding Ricci solitons on specific topologies.

This paper classifies all expanding Ricci solitons on surfaces.

In this paper, we prove that expanding gradient Ricci solitons with (positively) pinched Ricci curvature are trivial ones. Namely, they are either compact or flat.

Study shows expanding Ricci solitons from specific metric cones.

Study expanding gradient Ricci solitons with Euclidean base.

No expanding breathers found in noncompact Ricci flows with certain curvature conditions.

The paper shows how to stabilize perturbed Kähler-Ricci solitons.

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…

In this paper, we study gradient Ricci expanding solitons $(X,g)$ satisfying $Rc=cg+D^2f,$ where $Rc$ is the Ricci curvature, $c<0$ is a constant, and $D^2f$ is the Hessian of the potential function $f$ on $X$. We show that for a gradient expanding soliton $(X,g)$ with non-negative Ricci curvature, the scalar curva…

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.

We show that expanding Kähler-Ricci solitons which have positive holomorphic bisectional curvature and are asymptotic to Kähler cones at infinity must be the U(n)-rotationally symmetric expanding solitons constructed by Cao.

We show that an expanding gradient Ricci solitons which is asymptotic to a cone at infinity in a certain sense must be rotationally symmetric.

We produce new examples of non-Kähler complete expanding gradient Ricci solitons on trivial vector bundles over a product of Einstein manifolds with positive scalar curvature.

This paper classifies Ricci solitons in complex hyperbolic spaces.

We show that at the level of formal expansions, any compact Riemannian manifold is the sphere at infinity of an asymptotically conical gradient expanding Ricci soliton.

The study provides estimates for curvature of gradient Ricci solitons.

New findings on gradient expanding Ricci solitons with finite scalar curvature ratio.

We introduce the notion of Canonical Expanding Ricci Soliton, and use it to derive new Harnack inequalities for Ricci flow. This viewpoint also gives geometric insight into the existing Harnack inequalities of Hamilton and Brendle.

We show that gradient shrinking, expanding or steady Ricci solitons have potentials leading to suitable reference probability measures on the manifold. For shrinking solitons, as well as expanding soltions with nonnegative Ricci curvature, these reference measures satisfy sharp logarithmic Sobolev inequalities with low…

This paper provides a study of algebraic Ricci solitons in the pseudo-Riemannian case. In the Riemannian case, all nontrivial homogeneous algebraic Ricci solitons are expanding algebraic Ricci solitons. In this paper, we obtain a steady algebraic Ricci soliton and a shrinking algebraic Ricci soliton in the Lorentzian s…

Study of special Lorentzian Lie groups with 4D isometry group, finding all are non-gradient expanding Ricci solitons.

Characterizes potential function of almost conformal Ricci solitons on Sasakian manifolds.

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.

The paper establishes curvature estimates for solitons in higher dimensions.

Study expanding Ricci solitons on vector bundles, reducing to Higgs bundle equations.

The paper estimates curvature for specific 4D Ricci solitons.

We study the geometry at infinity of expanding gradient Ricci solitons of dimension greater than two with finite asymptotic curvature ratio without curvature sign assumptions. We mainly prove that they have a cone structure at infinity.

Study on non-gradient Ricci almost solitons in warped products.

We give necessary and sufficient conditions for a Kähler equivariant resolution of a Kähler cone, with the resolution satisfying one of a number of auxiliary conditions, to admit a unique asymptotically conical (AC) expanding gradient Kähler-Ricci soliton. In particular, it follows that for any $n\in\mathbb{N}_{0}$ and…

We produce new non-Kähler, non-Einstein, complete expanding gradient Ricci solitons with conical asymptotics and underlying manifold of the form $\R^2 \times M_2 \times \cdots \times M_r$, where $r \geq 2$ and $M_i$ are arbitrary closed Einstein spaces with positive scalar curvature. We also find numerical evidence for…

Survey paper analyzes curvature estimates for 4D gradient Ricci solitons.

Study shows instability of Kähler Ricci solitons and stability of orbifold singularities.

The paper examines Lorentz Ricci solitons on specific Lie groups.

In previous work, the authors studied the linear stability of algebraic Ricci solitons on simply connected solvable Lie groups (solvsolitons), which are stationary solutions of a certain normalization of Ricci flow. Many examples were shown to be linearly stable, leading to the conjecture that all solvsolitons are line…

We show that Lorentzian manifolds whose isometry group is of dimension at least $\frac{1}{2}n(n-1)+1$ are expanding, steady and shrinking Ricci solitons and steady gradient Ricci solitons. This provides examples of complete locally conformally flat and symmetric Lorentzian Ricci solitons which are not rigid.

New gradient Ricci solitons found for $SU(2)$ invariants.