Related papers: Transformations of Grassman Spaces
This text is about geometric structures imposed by robust dynamical behaviour. We explain recent results towards the classification of partially hyperbolic systems in dimension 3 using the theory of foliations and its interaction with…
A summary of the known results on integration theory on the space of connections modulo gauge transformations is presented and its significance to quantum theories of gauge fields and gravity is discussed. The emphasis is on the underlying…
We define and study the properties of $\gamma^{*}$-regular and $\gamma$-normal spaces. We also continue studying $\gamma_{o}$-compact spaces defined in [5].
A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.
We obtain new inversion formulas for the Radon transform and the corresponding dual transform acting on affine Grassmann manifolds of planes in $R^n$. The consideration is performed in full generality on continuous functions and functions…
Some aspects of the connection between differential geometry and multidimensional soliton equations are discussed.
We study several problems concerning conformal transformation on metric measure spaces, including the Sobolev space, the differential structure and the curvature-dimension condition under conformal transformations. This is the first result…
The usual examples of Bergman spaces consist of the closure of an algebra of holomorphic functions on a domain. One can also take the real part of such functions, but essentially one is looking at the same object. In this paper the author…
We give a construction of a Poisson transform mapping density valued differential forms on generalized flag manifolds to differential forms on the corresponding Riemannian symmetric spaces, which can be described entirely in terms of finite…
We investigate the modified gravity theories in terms of the effective dark energy models. We compare the cosmic expansion history and the linear growth in different models. We also study the evolution of linear cosmological perturbations…
We develop the theory of locally small spaces in a new simple language and apply this simplification to re-build the theory of locally definable spaces over structures with topologies.
The study of the structure of translational tilings has captivated mathematicians, scientists, and the general public for centuries and continues to thrive at the crossroads of analysis, combinatorics, dynamics, logic, number theory, and…
The paper surveys several results on the topology of the space of arcs of an algebraic variety and the Nash problem on the arc structure of singularities.
The theory of geometric structures on a surface with nonempty boundary can be developed by using a decomposition of such a surface into hexagons, in the same way as the theory of geometric structures on a surface without boundary is…
We overview main topics and ideas in spaces with their scalar curvatures bounded from below, and present a more detailed exposition of several known and some new geometric constraints on Riemannian spaces implied by the lower bounds on…
This is a commentary on two recent experimental papers in PNAS by Vivek et al. and Illing et al. that convincingly address an issue at the junction of two fundamental questions in glass physics: the role of the dimensionality of space on…
The linear isometries between weighted Banach spaces of continuous functions are considered. Some of well known theorems on isometries between spaces of continuous functions are proved and stated, but all they are in an appropriate form. In…
Following T. Suwa, we study unfoldings of algebraic foliations and their relationship with families of foliations, making focus on those unfoldings related to trivial families. The results obtained in the study of unfoldings are then…
Playing off against each other the real and complex structures, we elucidate the local structure of certain representation spaces in the world of Poisson geometry. Particular cases of these spaces arise as moduli spaces of semistable…
The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in machine learning, computer vision and image processing to low-rank matrix optimization problems,…