Related papers: Maximal Hamiltonian tori for polygon spaces
We give necessary and sufficient conditions for an orthogonal group defined over a field of characteristic not 2 to contain a maximal torus of a given type.
The concept of soliton, in its most general version, allows us to find canonical or distinguished elements on any set provided with an equivalence relation and an `optimal' tangent direction at each point. We study in this paper solitons on…
We obtain some equations for Hamiltonian-minimal Lagrangian surfaces in CP^2 and give their particular solutions in the case of tori.
We study the problem of rotating a simple polygon to contain the maximum number of elements from a given point set in the plane. We consider variations of this problem where the rotation center is a given point or lies on a line segment, a…
We show how to view the equations for a cohomogeneity one Ricci soliton as a Hamiltonian system with a constraint. We investigate conserved quantities and superpotentials, and use this to find some explicit formulae for Ricci solitons not…
Let G be a connected reductive group over the complex numbers with a fixed pinning. We define and study the totally positive part of the set of maximal tori of G.
In this paper we establish three basic equations for a general soliton structure on the Riemannian manifold $(M, <, >)$. We then draw some geometric conclusions with the aid of the maximum principle.
In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The…
This paper studies two topics concerning on the orthogonal complement of one dimensional subspace with respect to a given quadratic form on a vector space over a number field. One is to determine the invariants for the isomorphism class of…
We consider the global Morrey-type spaces with variable exponents and general function defining these spaces. In the case of unbounded sets, we prove boundedness of the Hardy-Littlewood maximal operator, potential type operator in these…
We determine a precise necessary and sufficient condition for completeness of the Hamiltonian vector field associated to a homogeneous cubic polynomial on a symplectic plane.
We calculate the maximal dimension of linear spaces of symmetric and hermitian matrices with given high rank, generalizing a well-known result of Adams {\em et al.}
We construct a family of flat isotropic non-homogeneous tori in $\mathbb{H}^n$ and $\mathbb{C} \mathrm{P}^{2n+1}$ and find necessary and sufficient conditions for their Hamiltonian minimality.
Let G be a compact group acting in a real vector space V. We obtain a number of inequalities relating the L^infinity norm of a matrix element of the representation of G with its L^p norm for p<infinity. We apply our results to obtain…
A possible generalisation is given to the meaning of maximal symmetry in the presence of torsion
The objective here is to find the maximum polygon, in area, which can be enclosed in a given triangle, for the polygons: parallelograms, rectangles and squares. It will initially be assumed that the choices are inscribed polygons, that is…
For a given smooth manifold, we consider the moduli space of Riemannian metrics up to isometry and scaling. One can define a preorder on the moduli space by the size of isometry groups. We call a Riemannian metric that attains a maximal…
We observe that a large part of the volume of a hyperbolic polyhedron is taken by a tubular neighbourhood of its boundary, and use this to give a new proof for the finiteness of arithmetic maximal reflection groups following a recent work…
In present paper, from the viewpoint of physical intuition we introduce a Hamiltonian system with multiscale rotation, which describes many systems, for example, the forced pendulum with fast rotation, weakly coupled $N$-oscillators with…
It is possible to have a packing by translates of a cube that is maximal (i.e.\ no other cube can be added without overlapping) but does not form a tiling. In the long running analogy of packing and tiling to orthogonality and completeness…