相关论文: Harmonic Hopf Constructions Between Spheres II
In the present paper, we derive several conditions of linear combinations and convolutions of harmonic mappings to be univalent and convex in one direction, one of them gives a partial answer to an open problem proposed by Dorff. The…
We prove a homological stability theorem for certain complements of symmetric spaces. This is a variant of a conjecture by Vakil and Matchett Wood for subspaces of $\mathrm{Sym}^n(X)$ where $X$ is an open manifold admitting a boundary. To…
We introduce a new map between configuration spaces of points in a background manifold - the replication map - and prove that it is a homology isomorphism in a range with certain coefficients. This is particularly of interest when the…
In this contribution we aim to study the stability boundaries of solutions at equilibria for a second-order oscillator networks with SN-symmetry, we look for non-degenerate Hopf bifurcations as the time-delay between nodes increases. The…
One of the most fundamental mathematical contributions of Garrett Birkhoff is the HSP theorem, which implies that a finite algebra B satisfies all equations that hold in a finite algebra A of the same signature if and only if B is a…
Bi-Hamiltonian structures are of great importance in the theory of integrable Hamiltonian systems. The notion of compatibility of symplectic structures is a key aspect of bi-Hamiltonian systems. Because of this, a few different notions of…
The proposition that band geometry alone can protect optical states against disorder has proven not merely theoretically elegant but experimentally incontrovertible. A key attribute of photonic topological systems is their capacity to…
We prove several unique continuation results for biharmonic maps between Riemannian manifolds.
We study the relationship between the partial synchronous (PaS) state and the coupling structure in general dynamical systems. By the exact proof, we find the sufficient and necessary condition of the existence of PaS state for the coupling…
Let $H$ be a Hopf algebra and $\mathcal{LR}(H)$ the category of Yetter-Drinfel'd-Long bimodules over $H$. We first give sufficient and necessary conditions for $\mathcal{LR}(H)$ to be symmetry and pseudosymmetry, respectively. We then…
We prove that, in general, given a $p$-harmonic map $F:M\to N$ and a convex function $H:N\to\mathbb{R}$, the composition $H\circ F$ is not $p$-subharmonic. By assuming some rotational symmetry on manifolds and functions, we reduce the…
We present a necessary and sufficient condition for the topological equivalence of a continuous function on a plane to a projection onto one of coordinates.
We show the existence of homoclinic type solutions of second order Hamiltonian systems with a potential satisfying a relaxed superquadratic growth condition and a forcing term that is sufficiently small in the space of square integrable…
Finding necessary and sufficient conditions for isomorphism between two semigroups of order-preserving transformations over an infinite domain with restricted range was an open problem in \cite{FHQS}. In this paper, we show a proof strategy…
We give a necessary and sufficient condition for the mapping class group of the pair of the 3-sphere and a graph embedded in it to be isomorphic to the topological symmetry group of the embedded graph.
We show that two open books in a given closed, oriented three-manifold admit isotopic stabilizations, where the stabilization is made by successive plumbings with Hopf bands, if and only if their associated plane fields are homologous.…
In this paper, we construct a bialgebraic and further a Hopf algebraic structure on top of subgraphs of a given graph. Further, we give the dual structure of this Hopf algebraic structure. We study the algebra morphisms induced by graph…
We prove that some of the classical homological stability results for configuration spaces of points in manifolds can be lifted to motivic cohomology.
A plane non-parallel flow in a square fluid domain exhibits an odd number of vortices. A spectral structure is found to have a non-real solution of the spectral problem linearized around the flow. With the use of this structure, Hopf…
We consider the general problem of constructing the structure of a smooth manifold on a given space of loops in a smooth finite dimensional manifold. By generalising the standard construction for smooth loops, we derive a list of conditions…