Related papers: Point vortices for inviscid generalized surface qu…
We investigate the presence of vortices in generalized Maxwell-Higgs models with a hidden sector. The model engenders $U(1)\times U(1)$ symmetry, in a manner that the sectors are coupled via the visible magnetic permeability depending only…
We investigate the bulk hydrodynamics of the chiral vortex matter on an arbitrary closed surface, extending the ideas of [20, 41]. Placing this important example of a chiral medium onto a curved geometry reveals the geometric nature of odd…
We investigate the behaviour of vertices and inflexions on 1-parameter families of curves on smooth surfaces in the 3-space, which include a singular member. In particular, we discuss the context where the curves evolve as sections of a…
We prove a hyperplane inequality for the surface area of projection bodies.
We establish that smooth, geometrically integral projective varieties of small degree are not pointless in suitable solvable extensions of their field of definition, provided that this field is algebraic over $\Bbb Q$.
We prove a topological rigidity theorem for closed hypersurfaces of the Euclidean sphere and of an elliptic space form. It asserts that, under a lower bound hypothesis on the absolute value of the principal curvatures, the hypersurface is…
This paper is devoted to investigating the rotating Boussinesq equations of inviscid, incompressible flows with both fast Rossby waves and fast internal gravity waves. The main objective is to establish a rigorous derivation and…
We prove persistence of the regularity of the boundary of vortex patches for a large class of transport equations in the plane. The velocity field is given by convolution of the vorticity with an odd kernel, homogeneous of degree $-1$ and…
Topological vortices in relativistic gauge theories in flat three-dimensional spacetime are investigated. We consider the symmetry $\rm{U(1)}\times...\times \rm{U(1)}$, and for each $\rm{U(1)}$ subgroup, a complex scalar field transforming…
An old theorem, due to Graustein, asserts that the average curvature of a plane oval is attained at least at four points. We present a proof by way of wave propagation and extend this result to the spherical and hyperbolic geometries - in…
The aim of this paper is to prove a fixed point theorem on a generalised cone metric spaces for maps satisfying general contractive type conditions.
A brief review is given of recent developments in the study of surface critical phenomena from the viewpoint of exactly solved lattice models. These developments include exact results for the polymer adsorption transition and the surface…
This article is a survey article on geometric group theory from the point of view of a non-expert who likes geometric group theory and uses it in his own research. The sections are: classical examples, basics about quasiisometry,properties…
Quadratic points of a surface in the projective 3-space are the points which can be exceptionally well approximated by a quadric. They are also singularities of a 3-web in the elliptic part and of a line field in the hyperbolic part of the…
We consider a generalized Gauss sum supported on matrices over a number field. We evaluate this Gauss sum and relate it to the number of totally isotropic subspaces of related quadratic spaces. Then we consider a further generalization of…
We consider the mean curvature flow of a closed hypersurface in the complex or quaternionic projective space. Under a suitable pinching assumption on the initial data, we prove apriori estimates on the principal curvatures which imply that…
A concept of abstract inductive definition on a complete lattice is formulated and studied. As an application, a constructive and predicative version of Tarski's fixed point theorem is obtained.
We get new results (and rederive some know ones) on smooth surfaces in $\mathbb{R}^n$ by unifying several view points into a coherent general view. Namely, we show and use new relations of the evolute (caustic) with the curvature ellipse,…
We introduce a new technique for proving the classical Stable Manifold theorem for hyperbolic fixed points. This method is much more geometrical than the standard approaches which rely on abstract fixed point theorems. It is based on the…
We present a formal derivation of the inviscid 3D quasi-geostrophic system (QG) from primitive equations on a bounded, cylindrical domain. A key point in the derivation is the treatment of the lateral boundary and the resulting boundary…