Related papers: Periods of Morse--Smale diffeomorphisms on $\mathb…

Periodic points are points on Veech surfaces, whose orbit under the group of affine diffeomorphisms is finite. We characterise those points as being torsion points if the Veech surfaces is suitably mapped to its Jacobian or an appropriate…

We give criteria for Morin singularities for germs of maps into lower dimensions. As an application, we study the bifurcation of Lefschetz singularities.

We consider the class of compact Riemann surfaces which are ramified coverings of the Riemann sphere $\hat{\mathbb{C}}$. Based on a triangulation of this covering of the sphere $\mathbb{S}^2\cong \hat{\mathbb{C}}$ and its stereographic…

A localisation of the category of n-manifolds is introduced by formally inverting the connected sum construction with a chosen n-manifold Y. On the level of automorphism groups, this leads to the stable diffeomorphism groups of n-manifolds.…

We present a new method to compare the shapes of genus-zero surfaces. We introduce a measure of mutual stretching, the symmetric distortion energy, and establish the existence of a conformal diffeomorphism between any two genus-zero…

We revisit the moving least squares (MLS) approximation scheme on the sphere $\mathbb S^{d-1} \subset \mathbb R^d$, where $d>1$. It is well known that using the spherical harmonics up to degree $L \in \mathbb N$ as ansatz space yields for…

We construct embedded minimal surfaces which are $n$-periodic in $\mathbb{R}^n$. They are new for codimension $n-2\ge 2$. We start with a Jordan curve of edges of the $n$-dimensional cube. It bounds a Plateau minimal disk which Schwarz…

Diffeomorphisms can be seen as automorphisms of the algebra of functions. In the matrix regularization, functions on a smooth compact manifold are mapped to finite size matrices. We consider how diffeomorphisms act on the configuration…

This paper studies the geometry of the group of all co-Hamiltonian diffeomorphisms of a compact cosymplectic manifold $(M, \omega, \eta)$. The fix-point theory for co-Hamiltonian diffeomorphisms is studied, and we use Arnold's conjecture to…

We demonstrate the existence of branched immersed 2-spheres with prescribed mean curvature, with controlled Morse index and with arbitrary codimensions in closed Riemannian manifold $N$ admitting finite fundamental group, where $\pi_k(N)…

We investigate periodic diffeomorphisms of non-compact aspherical manifolds (and orbifolds) and describe a class of spaces that have no homotopically trivial periodic diffeomorphisms. Prominent examples are moduli spaces of curves and…

We construct an explicit diffeomorphism taking any fibration of a sphere by great circles into the Hopf fibration, using elementary geometry--indeed the diffeomorphism is a local (differential) invariant, algebraic in derivatives.

We classify the sets of natural numbers $n$ for which certain dynamical systems $(X,f)$ on a compact metric space $X$ have a periodic point of (least) period $n$. Interest in this question dates back to Sharkovskii's theorem for continuous…

Let M be a weakly monotone symplectic manifold, and H be a time-dependent Hamiltonian; we assume that the periodic orbits of the corresponding time-dependent Hamiltonian vector field are non-degenerate. We construct a refined version of the…

We define the group of almost periodic diffeomorphisms on $\mathbb{R}^n$ and on an arbitrary Lie group. We then study the properties of its Riemannian and Lie group exponential maps and provide applications to fluid equations. In…

This paper investigates the moment-angle manifolds whose cohomology ring is isomorphic to that of a connected sum of sphere products. We first give a example of moment-angle manifolds corresponding to a 4 dimentional simplicial polytope. It…

We show that for an arbitrarily given closed Riemannian manifold $M$ admitting a point $p \in M$ with a single cut point, every closed Riemannian manifold $N$ admitting a point $q \in N$ with a single cut point is diffeomorphic to $M$ if…

In this paper, we have determined the orbit spaces of free involutions on a finitistic space having mod 2 cohomology of the product of three spheres $\mathbb{S}^n\times \mathbb{S}^m \times \mathbb{S}^l, 1 \leq n \leq m \leq l$. This paper…

We study minimal timelike surfaces in $\mathbb R^3_1$ using a special Weierstrass-type formula in terms of holomorphic functions defined in the algebra of the double (split-complex) numbers. We present a method of obtaining an equation of a…

We study the global Lipschitz character of minimisers of the Dirichlet energy of diffeomorphisms between doubly connected domains with smooth boundaries from Riemann surfaces. The key point of the proof is the fact that minimisers are…