Related papers: A characterization of the grim reaper cylinder
We show that any closed connected hypersurface in $\mathbb{R}^4$ with entropy less than or equal to that of the round cylinder is smoothly isotopic to the standard three-sphere.
We prove that a steady gradient Ricci soliton is either Ricci flat with a constant potential function or a quotient of the product steady soliton $N^{n-1}\times\mathbb{R}$, where $N^{n-1}$ is Ricci flat, or isometric to the Bryant soliton…
In this work, we study metrics which are both homogeneous and Ricci soliton. If there exists a transitive solvable group of isometries on a Ricci soliton, we show that it is isometric to a solvsoliton. Moreover, unless the manifold is flat,…
The three-dimensional topological insulator \ce{Bi2Te3} differs from other topological insulators in the \ce{Bi2Se3} family in that the effective Hamiltonian of its surface states on a flat semi-infinite slab requires the addition of a…
It is demonstrated that a C^1-unipotent map is globally equivalent to the linear translation T(x,y)=(x+1,y), if the map is fixed point free Similarly, it is proved not only that the fixed point set induced by a C^1-unipotent has no isolated…
We prove that every $C^1$ three-dimensional flow with positive topological entropy can be $C^1$ approximated by flows with homoclinic orbits. This extends a previous result for $C^1$ surface diffeomorphisms \cite{g}.
The slow dynamics of topological solitons in the CP^1 sigma-model, known as lumps, can be approximated by the geodesic flow of the L^2 metric on certain moduli spaces of holomorphic maps. In the present work, we consider the dynamics of…
We consider a ground state (soliton) of a Hamiltonian PDE. We prove that if the soliton is orbitally stable, then it is also asymptotically stable. The main assumptions are transversal nondegeneracy of the manifold of the ground states,…
Recent work has shown that if an isostatic bar and joint framework possesses non-trivial symmetries, then it must satisfy some very simply stated restrictions on the number of joints and bars that are `fixed' by various symmetry operations…
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…
A periodic tangle is a one-dimensional submanifold in $\mathbb{R}^3$ that has translational symmetry in one, two or three transverse directions. A periodic tangle can be seen as the universal cover of a link in the solid torus, the…
Let $S$ be a (topological) compact closed surface of genus two. We associate to each translation surface $(X,\omega) \in \mathcal{H}(2)\sqcup\mathcal{H}(1,1)$ a subgraph $\hat{\mathcal{C}}_{\rm cyl}$ of the curve graph of $S$. The vertices…
Soliton solutions with cylindrical symmetry are investigated within the nonlinear $\sigma $-model disregarding the Skyrme-stabilization term. The solitons are stabilized by quantization of collective breathing mode and collapse in the…
In this paper, we classify n-dimensional (n>2) complete noncompact locally conformally flat gradient steady solitons. In particular, we prove that a complete noncompact non-flat conformally flat gradient steady Ricci soliton is, up to…
We establish a symmetry principle for asymptotically cylindrical steady gradient Ricci solitons (GRSs) and asymptotically conical expanding GRSs with homogeneous links. Using this, we show that the Bryant steady soliton is the unique…
We consider the Poisson cylinder model in ${\mathbb R}^d$, $d\ge 3$. We show that given any two cylinders ${\mathfrak c}_1$ and ${\mathfrak c}_2$ in the process, there is a sequence of at most $d-2$ other cylinders creating a connection…
We prove that the homology of the mapping class groups of non-orientable surfaces stabilizes with the genus of the surface. Combining our result with recent work of Madsen and Weiss, we obtain that the classifying space of the stable…
Let $D$ be a non-pseudoconvex open set in $\C^3$ and $S$ be the union of all two-dimensional planes with non-empty and non-pseudoconvex intersection with $D.$ Sufficient conditions are given for $\C^3\setminus S$ to belong to a complex…
This note is devoted to the study of the homology class of a compact Poisson transversal in a Poisson manifold. For specific classes of Poisson structures, such as unimodular Poisson structures and Poisson manifolds with closed leaves, we…
We study the orbifold Gromov-Witten theory of the quotient C^3/Z_3 in all genera. Our first result is a proof of the holomorphic anomaly equations in the precise form predicted by B-model physics. Our second result is an exact crepant…