Related papers: Translating solitons $C^1-$asymptotic to two half-…
We show that plane bipolar posets (i.e., plane bipolar orientations with no transitive edge) and transversal structures can be set in correspondence to certain (weighted) models of quadrant walks, via suitable specializations of a bijection…
In this note we develop a half-space model for the pseudo-hyperbolic space $\mathbb{H}^{p,q}$, for any $p,q$ with $p\geq 1$. This half-space model embeds isometrically onto the complement of a degenerate totally geodesic hyperplane in…
We show that any diffeomorphism of a compact manifold can be C1 approximated by diffeomorphisms exhibiting a homoclinic tangency or by diffeomorphisms having a partial hyperbolic structure.
We study the continuation of periodic orbits from various compound of homoclinics in classical system. Together with the homoclinics, the periodic orbits make up a $C^1$-smooth, normally hyperbolic invariant cylinder with holes. It plays a…
This paper is devoted to the classification problems concerning extended deformations of convex polyhedra and real hyperplane arrangements in the following senses: combinatorial equivalence of face posets, normal equivalence on normal fans…
We introduce multipole soliton complexes in optical lattices induced by nondiffracting parabolic beams. Despite the symmetry-breaking dictated by the curvature of the lattice channels, we find that complex, asymmetric higher-order states…
We introduce a setting based on the one-dimensional (1D) nonlinear Schroedinger equation (NLSE) with the self-focusing (SF) cubic term modulated by a singular function of the coordinate, |x|^{-a}. It may be additionally combined with the…
Solitons in one-dimensional parity-time (PT)-symmetric periodic potentials are studied using exponential asymptotics. The new feature of this exponential asymptotics is that, unlike conservative periodic potentials, the inner and outer…
In this paper we prove the existence of families of n-dimensional complete embedded minimal submanifolds of C^n with a prescribed configuration of k>1 asymptotic planes. These submanifolds are obtained by desingularizing the intersection of…
Denote by $N_{\ell}(n)$ the number of $\ell$-tuples of elements in the symmetric group $S_n$ with commuting components, normalized by the order of $S_n$. In this paper, we prove asymptotic formulas for $N_\ell(n)$. In addition, general…
Relativistic scalar field theories with a conserved global charge Q possess often (meta)stable spherically symmetric soliton solutions, called Q-balls. We elaborate on the perfect formal analogy which exists between Q-balls, and spherically…
We describe the possible holonomy groups of simply connected irreducible non-locally symmetric pseudo-Riemannian spin manifolds which admit parallel spinors.
It is extended a result due to B. Guan and J. Spruck on the asymptotic Plateau's problem for CMC radial graphs in hyperbolic space to horizontal CMC graphs.
We extend the notion of polar duality to pairs of transverse Lagrangian planes in the standard symplectic space. This allows us to show that polar duality has a natural interpretation in terms of symplectic geometry. We apply our results to…
We continue our study on the pairs of singular Calabi--Yau varieties arising from double covers over semi-Fano toric manifolds. In this paper, we first investigate singular CY double covers of \(\mathbb{P}^{3}\) branched along (1) a union…
In this paper we establish a one-to-one correspondence between $S^1$-gerbes with connections, on the one hand, and their holonomies, for simply connected manifolds, or their parallel transports, in the general case, on the other hand. This…
We extend the technique of asymptotic series matching to exponential asymptotics expansions (transseries) and show that the extension provides a method of finding singularities of solutions of nonlinear differential equations, using…
We prove that for $C^{1+\theta}$, $\theta$-bunched, dynamically coherent partially hyperbolic diffeomorphisms, the stable and unstable holonomies between center leaves are $C^1$ and the derivative depends continuously on the points and on…
We develop the Lorentzian geometry of a crooked halfspace in 2+1-dimensional Minkowski space. We calculate the affine, conformal and isometric automorphism groups of a crooked halfspace, and discuss its stratification into orbit types,…
We show that the resolvent of the Laplacian on asymptotically hyperbolic spaces extends meromorphically with finite rank poles to the complex plane if and only if the metric is `even' (in a sense). If it is not even, there exist some cases…