Related papers: 3D flying wings for any asymptotic cones

We prove the existence of a one-parameter family of pairwise non-isometric, complete, positively curved, steady generalized Ricci solitons of gradient type on $\mathbb{R}^3$ that are invariant under the natural cohomogeneity one action of…

Let $(M^n,g,\nabla f)$, $n\geq 3$, be an expanding gradient Ricci soliton with nonnegative sectional curvature whose asymptotic cone is isometric to $C(\mathbb{S}^{n-1}(c))$ where $\mathbb{S}^{n-1}(c)$ is the standard $(n-1)$-sphere of…

In this note, we prove that a 3-dimensional steady Ricci soliton is rotationally symmetric if its scalar curvature $R(x)$ satisfies $$\frac{C_0^{-1}}{\rho(x)}\le R(x)\le \frac{C_0}{\rho(x)}$$ for some constant $C_0>0$, where $\rho(x)$…

In this paper, we will study the asymptotic geometry of 4-dimensional steady gradient Ricci solitons under the condition that they dimension reduce to $3$-manifolds. We will show that such 4-dimensional steady gradient Ricci solitons either…

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.

Starting from the Siklos waves in general relativity with a cosmological constant, interpreted as gravitational waves on the anti-de Sitter background, a new class of exact torsion waves is constructed in the framework of three-dimensional…

For a shrinking Ricci soliton with Ricci curvature convergent to zero at infinity, it is proved that it must be asymptotically conical.

We construct string backgrounds in dimension 2 which connect the Hamilton cigar to the round sphere. Specifically, we construct a 1-parameter family of rotationally symmetric steady gradient Ricci-Yang-Mills solitons on surfaces, where we…

We prove that a shrinking gradient Ricci soliton which is asymptotic to a K\"ahler cone along some end is itself K\"ahler on some neighborhood of infinity of that end. When the shrinker is complete, it is globally K\"ahler.

In this note, we shall investigate the asymptotic curvature estimate on steady Ricci solitons.

We show that if a shrinking soliton is asymptotic to a cone along an end then the isometry group of the cross-section of the cone embeds in the isometry group of the end of the shrinker. We also provide sufficient conditions for the…

In this paper we consider $4$-dimensional steady soliton singularity models, i.e., complete steady gradient Ricci solitons that arise as the rescaled limit of a finite time singular solution of the Ricci flow on a closed $4$-manifold. In…

In this paper, we give a description for steady Ricci solitons with a linear decay of sectional curvature. In particular, we classify all 3-dimensional steady Ricci solitons and 4-dimensional $\kappa$-noncollpased steady Ricci solitons with…

In this paper, we extend the work of Cao-Chen [9] on Bach-flat gradient Ricci solitons to classify $n$-dimensional ($n\ge 5$) complete $D$-flat gradient steady Ricci solitons. More precisely, we prove that any $n$-dimensional complete…

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…

This paper investigates the formation of fixed-wing UAVs in 3D, which communicate via a directed acyclic graph. Different from common formation problems, we consider the roto-translation invariant (RTI) formation, where the…

We develop a method for constructing complete gradient Ricci solitons realized as fiber bundles endowed with warped metrics, and we establish necessary and sufficient conditions for their existence. As an application, we present new…

We construct "Flying Saucer" solitons in supersymmetric N=2 gauge theory which is known to support BPS domain walls with a U(1) gauge field localized on its worldvolume. We demonstrate that this model supports exotic particle-like solitons…

A lower-bound estimate of injectivity radius for complete Riemannian manifolds is discussed in a pure geometric viewpoint and is applied to study tangent cones at infinity of certain gradient Ricci solitons. We also study the asymptotic…

Let $S$ be a finite set of points in the plane that are in convex position. We present an algorithm that constructs a plane $\frac{3+4\pi}{3}$-spanner of $S$ whose vertex degree is at most 3. Let $\Lambda$ be the vertex set of a finite…