arXiv research

Unique steady and expanding solitons with spherical links identified.

Study on steady solitons' curvature behavior near infinity.

The paper studies bowl solitons and their asymptotic expansions.

Study classifies 4D Ricci solitons with specific curvature conditions.

Study of 4D Ricci solitons with symmetry, finding precise geometric asymptotics.

New expanding Ricci solitons found starting in dimension four.

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 steady gradient Ricci solitons are all O(2)-symmetric.

Uniqueness proven for specific types of geometric structures.

The paper pinches curvature in expanding Ricci solitons.

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

New degree theory proves existence of solitons on 4D manifolds.

Ricci flow modelled on specific singularities on closed manifolds.

Study on scalar curvature decay in four-dimensional steady solitons.

Researchers found infinitely many non-collapsed steady Ricci solitons on complex line bundles.

Study on Einstein solitons with bounds and asymptotic behavior.

Study finds solitons on curved spaces with varying behavior.

We produce new non-Kähler complete steady gradient Ricci solitons whose asymptotics combine those of the Bryant solitons and the Hamilton cigar. We also obtain a family of complete Ricci-flat metrics with asymptotically locally conical asymptotics. Finally, we obtain numerical evidence for complete steady soliton struc…

We show that if two gradient Ricci solitons are asymptotic along some end of each to the same regular cone, then the soliton metrics must be isometric on some neighborhoods of infinity of these ends. Our theorem imposes no restrictions on the behavior of the metrics off of the ends in question and in particular does no…

Ancient Ricci flows with asymptotic solitons have uniform bounds and inequalities.

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

Existence of non-Einstein, non-shrinking Ricci solitons on quaternionic and octonionic spaces.

Study on solitons in specific geometric manifolds, proving manifold properties and presenting examples.

In this paper, we analyze the asymptotic behavior of $κ$-noncollapsed and positively curved steady Ricci solitons and prove that any $n$-dimensional $κ$-noncollapsed steady Kähler-Ricci soliton with non-negative sectional curvature must be flat.

In this paper we prove that any asymptotically cylindrical gradient shrinking Ricci soliton is isometric to a cylinder.

The paper classifies solitons for a specific type of flow.

New steady gradient Ricci solitons found with specific symmetry.

The paper studies steady solitons with curvature decay and proves their smoothness.

We provide a detailed description of solutions of Curve Shortening in $\R^n$ that are invariant under some one-parameter symmetry group of the equation, paying particular attention to geometric properties of the curves, and the asymptotic properties of their ends. We find generalized helices, and a connection with curv…

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 show that a three-dimensional steady gradient Ricci soliton which is asymptotic to the Bryant soliton in a suitable sense must be isometric to the Bryant soliton.

In this paper, we study the existence, uniqueness and asymptotic behavior of rotationally symmetric translating solitons of the mean curvature flow in Minkowski space. We also study the asymptotic behavior and the strict convexity of general solitons of such flows.

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

Uniqueness proven for a specific type of complex manifold's solitons.

Study on asymptotic behavior of Taub-NUT type solitons and construction of new ALF Calabi-Yau metrics.

3D flying wings created for any angle asymptotic cones.

Backward propagation rules for warped products under Ricci flow.

Characterizes rotational solitons for curve shortening flow on revolution surfaces.

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.

Study of solitons in Laplacian flow on 7-manifolds.

Paper classifies 3D breathers and generalizes Ricci soliton 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 $\lim_{dist(O,x)\rightarrow\infty} |Sect|\cdot dist(O,x)^2=0$. Therefore, for such a soliton, we can show that it must have $\mathbb{R}^n$ as one of…

The paper proves convexity of certain solitons and expanders in high dimensions.

Study precise asymptotics of noncompact Type-IIb solutions to mean curvature flow.

Paper proves uniqueness of catenary cylinders based on their asymptotic shape.

We prove that the hyperplanes parallel to ${\bf e}_{n+1}$ are the unique examples of translating solitons $C^1-$asymptotic to two half-hyperplanes outside a vertical cylinder in $\R^{n+1}$.

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 other end. We prove that this is the only gradient soliton with this topology, prov…

Researchers found cylindrical steady gradient solitons in 3D.