相关论文: Kairvaire Problems in Stable Homotopy Theory

Given a smooth $s$-dimensional submanifold $S$ of $\mathbb{R}^{m+c}$ and a smooth distribution $D\supset TS$ of rank $m$ along $S$, we study the following geometric Cauchy problem: to find an $m$-dimensional rank-$s$ submanifold $M$ of…

We establish a Liouville type result for stable solutions for a wide class of second order semilinear elliptic equations in $\mathbb{R}^{n}$ with sign-changing nonlinearity $f$. Under the hypothesis that the equation does not have any…

The main objective of this work is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations (see's) and stochastic partial differential equations (spde's) near stationary solutions. Such…

Equivariant homotopy methods developed over the last 20 years lead to recent breakthroughs in the Borel isomorphism conjectures for Loday assembly maps in K- and L-theories. An important consequence of these algebraic conjectures is the…

We study the affine quasi-Einstein equation, a second order linear homogeneous equation, which is invariantly defined on any affine manifold. We prove that the space of solutions is finite-dimensional, and its dimension is a strongly…

A problem about Khovanov homology and 3-manifolds is discussed in this paper.

An isovariant map is an equivariant map between $G$-spaces which strictly preserves isotropy groups. We consider an isovariant analogue of Klein--Williams equivariant intersection theory for a finite group $G$. We prove that under certain…

For a closed Riemannian manifold of dimension $n\geq 3$ and a subgroup $G$ of the isometry group, we define and study the $G-$equivariant second Yamabe constant and we obtain some results on the existence of $G-$invariant nodal solutions of…

We consider the Cauchy problem for the defocusing complex mKdV equation with finite density initial data \begin{align*} &q_t+\frac{1}{2}q_{xxx}-3|q|^2q_{x}=0,\\ &q(x,0)=q_{0}(x) \sim \pm 1, \ x\to \pm\infty, \end{align*} which can be…

We study the representation theory of the nested instantons quiver presented in [1], which describes a particular class of surface defects in four-dimensional supersymmetric gauge theories. We show that the moduli space of its stable…

The need for the extra dimension in Kustaanheimo-Stiefel (KS) regularization is explained by the topology of the Hopf fibration, which defines the geometry and structure of KS space. A trajectory in Cartesian space is represented by a…

We show rational homological stability for the homotopy automorphisms and block diffeomorphims of iterated connected sums of products of spheres. The spheres can have different dimension, but need to satisfy a certain connectivity…

We give formulas for calculating the unramified Brauer group of a homogeneous space $X$ of a semisimple simply connected group $G$ with finite geometric stabilizer $\bar F$ over a wide family of fields of characteristic 0. When $k$ is a…

In this paper a geometric approach toward stable homotopy groups of spheres, based on the Pontrjagin-Thom construction is proposed. From this approach a new proof of Hopf Invariant One Theorem by J.F.Adams for all dimensions except…

We show that, given a complete Liouville manifold, any homogeneous quasi-morphism on its Hamiltonian group, which satisfies a strengthened version of Hofer continuity called stability, must vanish. This partially addresses a conjecture due…

We investigate the problem of balanced embedding of a non-compact complex manifold into an infinite-dimensional projective space. In this paper we prove the existence of such an embedding in a model case. The strategy is by using a gradient…

Spectral problems are considered generated by the Sturm-Liouville equation on equilateral trees with the Dirichlet boundary conditions at the pendant vertices and continuity and Kirchhoff's conditions at the interior vertices. It is proved…

Motivated by recent experimental and numerical studies of coherent structures in wall-bounded shear flows, we initiate a systematic exploration of the hierarchy of unstable invariant solutions of the Navier-Stokes equations. We construct a…

We make an exposition of recent research on $(-1)$-homogeneous solutions of the three-dimensional incompressible stationary Navier-Stokes equations with singular rays. We also discuss properties of such solutions that are axisymmetric with…

We discuss an eigenvalue problem which arises in the studies of asymptotic stability of a self-similar attractor in the sigma model. This problem is rather unusual from the viewpoint of the spectral theory of linear operators and requires…