Related papers: Point vortices for inviscid generalized surface qu…

We prove that rigid representations of the fundamental group of a surface into the group of oreintation-preserving homeomorphisms of the circle are geometric, thereby establishing a converse statement of a theorem by the first author.

As is well-known, two-dimensional and three-dimensional superfluids under rotation can support topological excitations such as quantized point vortices and line vortices respectively. Recently, we have studied how, in a hypothetical…

We present numerical studies of wetting on various topographic substrates, including random topographies. We find good agreement with recent predictions based on an analytical interface-displacement-type theory \cite{Herminghaus2012,…

We formulate and prove a weighted version of Zariski's hyperplane section theorem on the topological fundamental groups of the complements of hypersurfaces in a projective space. As an application, we calculate fundamental groups of the…

We prove that strong finite total curvature complete hypersurfaces of (n+1)-euclidean space are proper and diffeomorphic to a compact manifold minus finitely many points. With an additional condition, we also prove that the Gauss map of…

In this paper we prove some new fixed point theorems for multivalued mappings on orbitally complete uniform spaces.

We explore the conditions required for isolated vortices to exist in sheared zonal flows and the stability of the underlying zonal winds. This is done using the standard 2-layer quasigeostrophic model with the lower layer depth becoming…

We investigate the problem of finding complete strictly convex hypersurfaces of constant curvature in hyperbolic space with a prescribed asymptotic boundary at infinity for a general class of curvature functions.

We consider the detailed dynamics of an array of quantised superfluid vortices in the framework of general relativity, as required for quantitative modelling of realistic neutron star cores. Our model builds on the variational approach to…

The purpose of this note is to give an (esentially optimal) effective version of Matsusaka's Big theorem for smooth projective surfaces.

We prove that if the initial hypersurface of the mean curvature flow in spheres satisfies a sharp pinching condition, then the solution of the flow converges to a round point or a totally geodesic sphere. Our result improves the famous…

We give a new proof of McShane's classification of simple cuspidal geodesics, using simple equivariant methods in the hyperbolic plane.

Let $M$ be a closed hyperbolic $3$-manifold. A homotopy class $[S]$ of surfaces in $M$ is filling if any representative cuts $M$ into components contractible in $M$. We prove that there exist $\epsilon_0, g_0>0$ such that every homotopy…

We provide rigorous evidence of the fact that the modified Constantin-Lax-Majda equation modeling vortex and quasi-geostrophic dynamics describes the geodesic flow on the subgroup of orientation-preserving diffeomorphisms fixing one point,…

In this paper, we prove that for any smooth hypersurface $Y$ of degree $d$ in $\mathbb{P}^{n+1}_k$, the cyclic $d$-fold cover $\widetilde{Y} \to \mathbb{P}^{n+1}_k$ branched along $Y$ completely characterizes $Y$ up to projective…

For a non-arithmetic Veech surface, it is known that the set points having finite orbit under the Veech group, called the set of periodic points, is finite. However, few examples of these periodic point sets have been computed. In what…

Numerical approximations of finite systems of vortices in the plane, collapsing to a point in finite time are studied. A fast method leading to highly accurate approximations is presented. The method is illustrated with an example of an…

In this note, we derive an asymptotically sharp upper bound on the number of lattice points in terms of the volume of centrally symmetric convex bodies. Our main tool is a generalization of a result of Davenport that bounds the number of…

The paper contains a general construction which produces new examples of non simply-connected smooth projective surfaces. We analyze the resulting surfaces and their fundamental groups. Many of these fundamental groups are expected to be…

We prove several new transversality results for formal CR maps between formal real hypersurfaces in complex space. Both cases of finite and infinite type hypersurfaces are tackled in this note.