Related papers: Rigidity and Flexibility in Poisson Geometry
We consider the motion of a two-dimensional body of arbitrary shape in a planar irrotational, incompressible fluid with a given amount of circulation around the body. We derive the equations of motion for this system by performing…
In this review article we discuss some of the applications of noncommutative geometry in physics that are of recent interest, such as noncommutative many-body systems, noncommutative extension of Special Theory of Relativity kinematics,…
Basic concepts and definitions in differential geometry and topology which are important in the theory of solitons and instantons are reviewed. Many examples from soliton theory are discussed briefly, in order to highlight the application…
We study geometric rigidity of a class of fractals, which is slightly larger than the collection of self-conformal sets. Namely, using a new method, we shall prove that a set of this class is contained in a smooth submanifold or is totally…
We discuss the concept of natural Poisson bivectors, which allows us to consider the overwhelming majority of known integrable systems on the sphere in framework of bi-Hamiltonian geometry.
We use the hamiltonian formalism to study the asymptotic structure of 3 dimensional gravity with a negative cosmological constant. We start by defining very general fall-off conditions for the canonical variables and study the implied…
The shape of semiflexible polymer rings is studied over their whole range of flexibility. Investigating the joint distribution of asphericity and nature of asphericity as well as their respective averages we find two distinct shape regimes…
General framework for Poisson homogeneous spaces of Poisson groups is introduced. Poisson Minkowski spaces are discussed as a particular example.
We study the rigidity of polyhedral surfaces using variational principle. The action functionals are derived from the cosine laws. The main focus of this paper is on the cosine law for a non-triangular region bounded by three possibly…
We report on recent developments in the dynamics and rigidity of infinite-volume homogeneous spaces, viewed through the lens of circles. By addressing four natural questions about circle packings, we highlight the interplay between…
We prove an analogue of Thurston's h-principle for $2$-dimensional foliations on manifolds of dimension bigger or equal to $4$, in the presence of a fiber-wise non-degenerate $2$-form. This helps us understand the flexibility of rank $2$…
We define and study slider-pinning rigidity, giving a complete combinatorial characterization. This is done via direction-slider networks, which are a generalization of Whiteley's direction networks.
We prove a result that can be applied to determine the finite-dimensional simple Poisson modules over a Poisson algebra and apply it to numerous examples. In the discussion of the examples, the emphasis is on the correspondence with the…
Inspired by the recent results toward Birkhoff conjecture (a rigidity property of billiards in ellipses), we discuss two rigidity properties of conics. The first one concerns symmetries of an analog of polar duality associated with an oval,…
In this paper we extend the almost complex Poisson structures from almost complex manifolds to almost complex Lie algebroids. Examples of such structures are also given and the almost complex Poisson morphisms of almost complex Lie…
We introduce and study suitable Poisson structures for four dimensional maps derived as lifts and specific periodic reductions of integrable lattice equations. These maps are Poisson with respect to these structures and the corresponding…
This paper is devoted to the study of Poisson structures on the Euclidean four dimensional space R4. By using the properties of the trace operator associated to a volumen form and the elementary vector calculus operations in R3, we give…
Flexibility and rigidity properties of steady (time-independent) solutions of the Euler, Boussinesq and Magnetohydrostatic equations are investigated. Specifically, certain Liouville-type theorems are established which show that suitable…
Several rigidity problems in toric topology are addressed in \cite{ma-su08}. In this paper, we survey results on those problems including recent development.
We study the Farrell and Jones Warping Deformation.