Related papers: Compact integral manifolds of differential systems
In this paper, we consider a fully nonlinear problem on manifolds with boundaries of negative admissible curvatures. As a consequence, we conclude the existence of certain types of metrics on the general differential manifolds with…
After a brief introduction to the Painlev\'{e} property for ordinary differential equations, we present a concise review of the various methods of singularity analysis which are commonly referred to as Painlev\'{e} tests. The tests are…
Some special solutions to the reflection equation are considered. These boundary matrices are defined on the common quantum space with the other operators in the chain. The relations with the Drinfeld twist are discussed.
We consider non-zero endomorphisms of the Dales and Davie algebras of infinitely differentiable functions on intervals in the real line. We discuss necessary and sufficient conditions for a selfmap of the interval to induce a compact…
We study the boundary of an affine invariant submanifold of a stratum of translation surfaces in a partial compactification consisting of all finite area Abelian differentials over nodal Riemann surfaces, modulo zero area components. The…
Inspired by the study of $V$-static manifold about classification, in this article, we apply the recent results obtained by Freitas and Gomes (Compact gradient Einstein-type manifolds with boundary, 2022) to prove the rigidity results for…
We consider a class of systems of difference equations defined on an elementary quadrilateral of the ${\mathbb{Z}}^2$ lattice, define their eliminable and dynamical variables, and demonstrate their use. Using the existence of infinite…
We study local bifurcations of periodic solutions to time-periodic (systems of) integrodifference equations over compact habitats. Such infinite-dimensional discrete dynamical systems arise in theoretical ecology as models to describe the…
The classical solvability of the initial-boundary problem for the Davey-Stewartson-II type system of equations is proved.
Let (M,g) be a compact Riemannian three-dimensional manifold with boundary. We prove the compactness of the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface.…
In the article we discuss the notion of the generalized invariant manifold introduced in our previous study. In the literature the method of the differential constraints is well known as a tool for constructing particular solutions for the…
For Riemannian manifolds with a smooth measure $(M, g, e^{-f}dv_{g})$, we prove a generalized Myers compactness theorem when Bakry--Emery Ricci tensor is bounded from below and $f$ is bounded.
This paper considers the existence of conformally compact Einstein metrics on 4-manifolds. A reasonably complete understanding is obtained for the existence of such metrics with prescribed conformal infinity, when the conformal infinity is…
We present quantum complexity lower and upper bounds for independent set problems in graphs. In particular, we give quantum algorithms for computing a maximal and a maximum independent set in a graph. We present applications of these…
If $f$ is an automorphism of a compact simply connected K\"ahler manifold with trivial canonical bundle that fixes a K\"ahler class, then the order of $f$ is finite. We apply this well known result to construct compact non-K\"ahler…
We analyze the boundaries of multiply connected Fatou components of transcendental maps by means of universal covering maps and associated inner functions. A unified approach is presented, which includes invariant Fatou components (of any…
We prove integral curvature bounds in terms of the Betti numbers for compact submanifolds of the Euclidean space with low codimension. As an application, we obtain topological obstructions for $\delta$-pinched immersions. Furthermore, we…
We obtain an embedding theorem for compact strongly pseudoconvex CR manifolds which are bounadries of some complete Hermitian manifolds. We use this to compactify some negatively curved Kaehler manifolds with compact strongly pseudoconvex…
We prove that the classical integrability condition for almost complex structures on finite-dimensional smooth manifolds also works in infinite dimensions in the case of almost complex structures that are real analytic on real analytic…
In the context of a finite measure metric space whose measure satisfies a growth condition, we prove "T1" type necessary and sufficient conditions for the boundedness of fractional integrals, singular integrals, and hypersingular integrals…